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734  BROADWAY,  NEW  YORK. 


A  TREATISE  ON  PHYSIOLOGY  AND  HYGIENE. 

FOR  EDUCATIONAL  INSTITUTIONS  AND  THE   GENERAL  READER. 

By  Joseph  C.  Hutchison,  M.D., 

President  of  the  New  York  Pathological  Society;  Vice-President  of  the  New  York 

Academy  of  Medicine;  Surgeon  to  the  Brooklyn  City  Hospital;  and  late 

President  of  the  Medical  Society  of  the  State  of  New  Yo/k. 


Fully  Illustrated  with  Numerous  Elegant  Engravings.    12mo.    300  pages. 


1.  Tlie  Plan  of  tlie  Work  is  to  present  the  leading  facts  and  principles 
of  human  Physiology  and  Hygiene  in  language  so  clear  and  concise  as 
to  be  readily  comprehended  by  pupils  in  schools  and  colleges,  as  well  as 
by  general  readers  not  familar  with  the  subject.  2.  The  Style  is  terse 
and  concise,  yet  intelligible  and  clear;  and  ail  useless  technicalities  have 
been  avoided.  3.  The  Range  of  Subjects  Treated  includes  those  on  which 
it  is  believed  all  persons  should  be  informed,  and  that  are  proper  in  a 
work  of  this  class.  4.  Ihe  Subject-matter. — The  attempt  has  been  made 
to  bring  the  subject-matter  up  to  date,  and  to  include  the  results  of  the 
most  valuable  of  recent  researches  to  the  exclusion  of  exploded  notions 
and  theories.  Neither  subject— Physiology  or  Hygiene— has  been  elabo- 
rated at  the  expense  of  the  other,  but  each  rather  has  been  accorded  its 
due  weight,  consideration,  and  space.  The  subject  of  Anatomy  is  in- 
cidentally treated  with  all  the  fullness  the  author  believes  necessary  in  a 
work  of  this  class.  5.  The  Engravings  are  numerous,  of  great  artistic 
merit,  and  are  far  superior  to  those  in  any  other  work  of  the  kind, 
among  them  being  two  elegant  colored  plates,  one  showing  the  Viscera 
in  Position,  the  other,  the  Circulation  of  the  Blood.  6.  The  Size  of  the 
work  will  commend  itself  to  teachers.  It  contains  about  300  pages,  and 
can  therefore  be  easily  completed  in  one  or  two  school  terms. 

The  publishers  are  confident  that  teachers  will  find  this  work  full  of  valuable 
matter,  much  of  which  cannot  be  found  elsewhere  in  a  class  manual,  and  so  pre- 
sented and  arranged  that  the  book  can  be  used  both  with  pleasure  and  success  in 
the  schoolroom.  

"  Many  of  the  popular  works  on  Physiology  now  in  use  in  schools,  academies,  and 
colleges,  do  not  reflect  the  present  state  of  the  science,  and  some  of  them  abound 
in  absolute  errors.  The  work  which  Dr.  Hutchison  has  given  to  the  public  is  free 
from  these  objectionable  features.  I  give  it  my  hearty  commendation." — Samuel 
Q.  Armor,  M.D.,  late  Professor  in  Michigan  University. 

"This  book  is  one  of  the  very  few  school  books  on  these  subjects  which  can  be 
unconditionally  recommended.  It  is  accurate,  free  from  needless  technicalities, 
and  judicious  m  the  practical  advice  it  gives  on  Hygienic  topics.  The  illustrations 
are  excellent,  and  the  book  is  well  printed  and  bound.  "—Boston  Journal  of 
Chemistry. 

"just  the  thing  for  schools,  and  I  sincerely  hope  that  it  may  be  appreciated  for 
what  it  is  worth,  for  we  are  certainly  in  need  of  books  of  this  kind."— Prof.  Austin 
Flint,  Jr.,  Professor  of  Physiology  in  Bellevne  Hosspital  Medical  College,  Neto  York 
City,  and  author  of  "  Physiology  of  Man,''''  etc.,  etc. 

"I  have  read  it  from  preface  to  colophon,  and  find  it  a  most  desirable  text-book 
for  schools.  Its  matter  is  judiciously  selected,  lucidly  presented,  attractively 
treated,  and  pointedly  illustrated  by  memorable  facts;  and,  as  to  the  plates  and 
diagrams,  they  are  not  only  clear  and  intelligible  to  beginners,  but  beautiful  speci- 
mens of  engraving.  I  do  not  see  that  any  better  presentation  of  the  subject  of 
?hysiology  could  be  given  within  the  same  compass." — Prof.  John  Ordronaux, 
*rofessor  of  Physiology  in  the  University  of  Vermont,  and  also  in  the  National 
Medical  College,  Washington,  D.  C. 

The  above  work  is  the  most  popular  work  on  the  above  subjects  yet  published.     It  is 
used  in  thousands  of  schools  with  marked  success. 

Published  by  CLARK  &  MAYNARD,  New  York. 


Digitized  by  the  Internet  Archive 

in  2007  with  funding  from 

Microsoft  Corporation 


http://www.archive.org/details/commercialarithmOOthomrich 


THOMSON'S    MATHEMATICAL    SERIES. 


tyv  Qt^e^l 


A 


COMMERCIAL 


ARITHMETIC; 

Academies,  Hioii   Schools,  Counting  Rooms; 


EMIES,    t^fGHtfeCHO^LS,    CoUN*T\ 
>\^    BUSINESSK.O 


G\* 


LLEGES 


James   B.   Thomson,   LL.  D., 

AUTHOR     OF     MATHEMATICAL     SERIES. 


NEW  YORK: 

Clark   &   Maynard,   Publishers, 

734   Broadway, 


THOMSON'S    NEW    ARITHMETICAL    SERIES 

IN    TWO     BOOKS. 


I.  First  Lessons  in  Arithmetic, 

Oral   and  Written.      Illustrated. 
(For  Primary  Schools.) 

II.  Complete  Graded  Arithmetic, 

Oral  and   Written.      In  one  Volume. 
(For  Schools  and   Academies.) 

Key  to  Complete  Graded  Arithmetic. 

(For  Teachers  only.) 

THOMSON'S    MATHEMATICAL    SERIES 

illustrated  table-book. 

new  rudiments  of  arithmetic. 

complete  intellectual  arithmetic, 
new  practical  arithmetic. 

KEY  TO  PRACTICAL  ARITHMETIC.  (For Teachers  only.) 

HIGHER    ARITHMETIC. 
PRACTICAL    ALGEBRA. 

KEY    TO    PRACTICAL    ALGEBRA.     (For  Teachers  only.) 

COLLEGIATE    ALGEBRA. 

KEY    TO    COLLEGIATE    ALGEBRA.     (For  Teachers  only.) 

COMMERCIAL    ARITHMETIC. 


Copyright,  1884,  by  M,  C.   Thomson. 


Smith  &  McDougal,  Electrotypees. 
82  Beekman  St.,  N.  Y. 


o=> 


I 


o  Teachers. 

"o    0     ^      =^» 


TF1HE  present  work  has  been  prepared  with  sole  reference  to  a  business 
education  in  its  higher  departments.  To  this  end,  subjects  which 
have  been  fully  explained  in  the  author's  elementary  works,  or  an 
equivalent,  and  with  which  the  student  is  supposed  to  be  familiar,  are 
omitted,  and  he  is  introduced  at  once  to  the  subject  in  hand.  All 
irrelevant  matter  is  rejected,  and  that  which  helps  towards  the  accomplish- 
ment of  the  object  is  adopted. 

A  large  amount  of  valuable  business  information  is  embodied  in  a 
concise  form,  and  presented  in  a  manner  to  be  easily  understood.  In  the 
fundamental  rules,  many  labor-saving  methods  of  operation  are  given  under 
the  appropriate  name  "  Counting  Room  Methods,"  so  called  from  the 
fact  that  rapid  computations  are  so  generally  practiced  by  expert  account- 
ants. These  methods  may  be  applied,  not  only  to  the  examples  given 
for  illustration  and  practice,  but  to  every  operation  involving  the  simple 
rules,  and  will  often  greatly  facilitate  arithmetical  calculations. 

A  variety  of  business  forms  are  introduced,  and  their  nature  and  uses 
explained,  in  order  to  assist  the  student  to  an  understanding  of  what 
constitutes  an  important  part  of  a  practical  business  life.  The  manner 
of  keeping  Book  Accounts,  Averaging  Payments,  Partnership  Settle- 
ments, etc.,  are  fully  explained  and  illustrated  by  examples  from  actual 
business  transactions. 

The  chapter  on  the  Metric  System  of  Weights  and  Measures  is 
made  prominent  in  the  body  of  the  book,  and  includes  all  the  latest 
recommendations  of  the  Metric  Bureau.  Examples  involving  a  knowledge 
of  its  applications  are  freely  scattered  through  the  book. 

The  subject  of  Analysis,  the  business  man's  specialty,  enters  largely 
into  the  elucidation  of  every  subject,  and  has  an  entire  chapter  devoted  to 
its  various  applications. 

The  facts  and  methods  given  on  many  commercial  subjects,  have  been 
procured  from  reliable  persons  who  are  thoroughly  versed  in  their  several 


IV 


To  Teachers. 


departments.  They  are  therefore  authentic  business  facts,  and  in  accord- 
ance with  present  usage. 

Special  care  has  been  devoted  to  the  chapter  on  Stocks  and  Bonds,  and 
to  Stock  Exchange  business,  which  is  a  full  and  reliable  summary  of 
affairs  as  now  conducted  on  the  New  York  Stock  Exchange.  The 
examples  embrace  true  specimens  of  daily  operations  in  Wall  Street. 

The  chapters  on  Banking,  Clearing  Houses,  and  Custom  House  busi- 
ness have  also  been  subjected  to  the  most  careful  scrutiny,  as  also,  Life 
Insurance,  Annuities,  Sinking  Funds,  etc. 

The  Commercial  Arithmetic  is  intended  to  follow  the  author's  Com- 
plete Graded,  or  the  Practical  Arithmetic,  taking  up  some  subjects  and 
carrying  them  forward  to  their  higher  applications,  and  treating  of  others 
which  are  beyond  the  limits  of  the  more  elementary  works.  In  subjects 
which  are  identical  with  the  Complete  Graded,  the  same  definitions  and 
principles  are  retained.  In  the  discussion  of  new  topics,  the  same  clear- 
ness, conciseness,  and  accuracy  of  style  have  been  strictly  adhered  to. 

The  examples  are  all  new,  and  have  been  selected  with  a  special  view 
to  their  practical  application  to  business,  and  not  as  a  trial  of  the 
mathematical  skill  of  the  learner. 

Many  thanks  are  due  to  the  gentlemen  of  the  Stock  and  Produce 
Exchanges ;  to  the  Collector  of  the  Port  of  New  York  and  his  associates ; 
to  the  Bankers,  Brokers,  and  Lawyers  who  have  so  kindly  given  valuable 
information  and  suggestions. 

It  is  hoped  the  Commercial  Arithmetic  will  creditably  fill  the  niche  for 
which  it  was  designed,  and  that  it  will  commend  itself  to  the  good  judg- 
ment of  teachers,  the  understanding  of  learners,  and  the  approval  of  busi- 
ness men. 

The  kindly  criticisms  of  all  will  be  gratefully  accepted,  and  their 
continued  favor  highly  appreciated. 

New  York,  March  1, 188k. 


CONTENTS 


PAGE 

Counting-Room    Exer- 
cises    7 

Addition 8 

Subtraction 9 

Multiplication  (Short  Methods)  11 

Division,  Contractions 16 

Divisibility  of  Numbers 18 

Factoring 18 

Cancellation 20 

Greatest  Common  Divisor 21 

Common  Multiples 23 

Weights  and  Measures. . .  26 

Weight  per  bushel  of  Grain 

and  Seeds 31 

To  Change  Dates  from  0.  S.  to 

N.  S 37 

United  States  Money 38 

Canada  Money 39 

English  Money,  French  Money.  40 
German  Money 41 

Metric  System 42 

Metric  Reduction 50 

Foreign      Weights     and 
Measures 53 

Reduction 55 

Denominate  Fractions 57 

Reduced  to  Lower  Denomina- 
tions    57 

Reduced  to  Higher  Denomina- 
tions   58 

Addition  of  Compound  Num- 
bers   59 

Subtraction      of      Compound 

Numbers.   60 

Exact     Time    between    Two 

Dates 61 

Compound  Multiplication 62 

Compound  Division 63 

Longitude 63 

Time  and  Longitude 65 


•PAGE 

Applications  of  Weights 

and  Measures 66 

Measurement  of  Rectangular 

Bodies 69 

Cisterns,  Bins,  etc 70 

Measurement  of  Lumber 71 

Masonry 73 

Applications    of    IT.    S. 

Money 73 

Methods  by  Aliquot  Parts. . .  74 

Bills  of  Merchandise 78 

Entry  Clerk's  Drill 80 

Percentage 81 

Applications  of  Percentage. . .  88 

Profit  and  Loss 88 

Trade  Discount 89 

Commission  and  Brokerage. .  91 

Insurance.         94 

Adjustment  of  Losses 98 

Taxes 100 

Interest 103 

General  Method 104 

Six  per  cent  Method 107 

Method  bv  Days 108 

Banker's  Method 109 

Accurate  Interest Ill 

Annual  Interest 112 

Partial  Payments 116 

U.  S.  Rule 117 

Mercantile  Method 118 

Connecticut  Rule  119 

Vermont  Rule 121 

New  Hampshire  Rule 122 

Interest  on  Sterling  Money . .   123 
Compound  Interest 124 

True  Discount 127 

Bank  Discount. 128 

Commercial  Paper 130 

Forms  of  Notes  and  Drafts.. .  133 


VI 


Contents. 


PAGE 

Averaging  Accounts 137 

Rules. — Product  Method, )        *  .^ 
Interest  Method  )"  140 

Cash  Balance 149 

Rule  for  Product  Method 150 

Rule  for  Interest  Method 151 

Account  Sales 154 

To  Find  Due  Date 156 

Partnership 158 

Bankruptcy 169 

General  Average 170 

General  Analysis 172 

Ratio 178 

Proportion 180 

By  Cause  and  Effect 182 

Compound  Proportion 184 

Partitive  Proportion 187 

Exchange 189 

Domestic  Exchange 190 

Foreign  Moneys  of  Account.  192 

Quotations  of  Foreign  Bills. .  193 

Foreign  Exchange 194 

Duties  or  Customs 199 

Custom  House  Business 200 

Import  Entries 203 

Course  of  Import    Entry  in 
N.  Y.  Custom  House 204 

Banks  and  Banking 206 

Bank  Account  Current 208 

Bank  Checks 209 

Clearing  Houses 211 

Savings  Banks 212 

Stocks 216 

United  States  Bonds 218 

National  Debt  of  U.  S 219 

Funded     Debt    of     Foreign 

Countries 220 

Stock  Exchanges 220 

Quotations. — Seller's  Option, )  9Q„ 

Buyer's  Option  ] 
Stock  Investments 223 


PAGE 

Produce  Exchanges 232 

Storage 234 

Life  Insurance 236 

Table  of  Rates 238 

Annuities 241 

Annuities  at  Compound  Inter- 
est    243 

Sinking  Funds 248 

Powers  and  Roots 251 

Square  Root 253 

Cube  Root 256 

Similar  Surfaces  and  Solids . .  258 

Mensuration 261 

Area  of  Plane  Figures 262 

Area  of  Triangles 264 

Circles 265 

Solids 268 

Gauging  of  Casks 273 

Tonnage  of  Vessels 275 

Grain  Measurement 275 

Lumber,  Doyle's  Rule 276 

Test  Questions 278 

Appendix 286 

Drill  in  Percentage 287 

Metric  Drill 289 

G.  c.  d.  of  Fractions  290 

L.  c.  in.  of  Fractions 291 

Table  of  Prime  Numbers 292 

Property  of  the  No.  9 293 

Contractions  in  Mult 293 

Table  of  Time,  in  days 295 

Mortality  Table 297 

Life  Estates 298 

Northampton  Table 299 

Business  Information 300 

Letters  of  Credit 304 

Instruments  under  Seal 304 

Book  Accounts 305 

Statute  of  Limitations 306 

Stock  Clearing  Houses 307 

Abbreviations  (Stocks) 308 

Miscellaneous  Examples 309 


Commercial  Arithmetic 


Art.  1.  The  student  of  Commercial  Arithmetic  is  presumed 
to  be  familiar  with  the  ordinary  operations  of  Common  Arith- 
metic. For  this  reason,  the  four  fundamental  rules,  fractions, 
decimals,  etc.,  are  omitted  in  this  work. 

COUNTING    ROOM    METHODS. 

2.  Facility  in  adding  is  of  the  first  importance  in  commer- 
cial life.  It  can  be  acquired  only  by  constant  practice,  and  a 
thorough  acquaintance  with  the  simple  combinations  of  num- 
bers. 

3.  In  adding  ledger  columns,  accountants  frequently  use  the 
following  methods : 


(Ex.  1.) 

(Ex.  2.) 

$784,306 

$346.82 

9.348 

204.36 

751.675 

56.07 

0.384 

207.00   814.25 

95.832 

862.741 
2204.206 

26.35 

460.48 

1.76 

$4708.492,  Ans. 

763.48  1252.07 

232  323 

Ans.   $2066.32 

Explanation. — Ex.  1.  Write  the  units'  figure  of  the  sum  of  each  col- 
umn under  the  column  added,  and  the  tens,  or  figures  carried,  below  as  in 
the  example.     In  adding,  name  only  results. 

Ex.  2.  The  second  method  divides  the  columns  into  parts,  adding  each 
part  separately  to  find  their  sum. 


8 


Counting  Rooyn  Metlwds. 


4.  Principles  of  Addition.— 1°.  Only  like  numbers  and 
like  orders  of  units  can  be  added  one  to  another. 

2°.  The  sum  is  the  same  in  whatever  order  numbers  may  be 
added. 

3.  Add  the  numbers  from  1  to  29  in  a  column.  From  29 
to  109.    From  109  to  199  inclusive. 


5.  Adding  two  or  more  columns  at  a  time. 

4.  Find- the  sum  of  29,  48,  37,  and  56. 

Explanation.— To  the  number  at  the  bottom  add  the 
tens,  then  the  unitsaLthe  next  number  above  it.     Thus, 

5G  and  ^0  are  KG,   ,n  <  7  arc  93,  and  40  are  133,  and  8  are 
14jS  Bo  afVilifflrand  9  are  170,  Ans. 


527,  432,  and  245, 


at  the  bottom,  245, 
the  units  of  the  next 
0  are  645,  and  30  are 
,  and  20  are  1197,  and 
30  are  1834,  and  9  are 


OPERATION. 

29 
48 
37 
56 

170 


Ans. 


S£pJ 


ind  the  sum 
Kins  at  a  time 


EXPLANATIO 

add  the  hundreds, 
pfPfoer  above  it ;  thus, 
675,  and  2  are 
?»rol204,  and 


Ine  following,  in  like  manner 


24 
32 

27 
23 
42 
91 
26 
34 
12 
67 
21 
53 
26 
78 


25 

82 
93 
54 
62 
58 
53 
24 
66 

J2 

26 

87 
72 
65 


(8.) 
46 
32 
17 
81 
28 
52 
23 
20 
71 
39 
18 
42 
73 
24 


519 
271 
436 
587 
333 
745 

52 
158 
232 
464 
643 

27 
235 
103 


(10.) 
607 
232 
211 
380 
578 
231 
145 
605 
760 
357 
544 
276 
803 
725 


adding  three 


OPERATION. 

639 
527 
432 
245 


Ans.  1843 

(n.) 
253 

12 
849 
436 
551 
349 
763 

37 
155 
676 
844 
232 
383 
918 


Counting  Room  Methods. 


6.  To  Add  Numbers  Horizontally. 

It  is  sometimes  convenient  to  add  numbers,  when  written 
horizontally,  instead  of  under  each  other. 

12.  Find  the  sum  of  428  +  253  +  647  +  926  +  425. 

Explanation. — Beginning  at  the  right,  add  the  units  of  all  the  num- 
bers, then  the  tens,  then  the  hundreds ;  the  sum  is  2679.  Arts. 

13.  Find  the  sum  of  2345  +  621  +  2417  +  385  -f-  6457. 

14.  Find  the  sum  of  325,  4623,  435,  2843,  7546. 

Note.— To  insure  accuracy,  the  addition  should  be  performed  by  differ- 
ent methods,  or  in  different  directions,  in  order  that  mistakes  made  by  one 
method  may  be  detected  by  another. 

7.  Principles  of  Subtraction. — 1°.  Only  like  numbers 
and  like  orders  of  units  can  be  subtracted  one  from  the  other. 

2°.   The  difference  and  subtrahend  are  equal  to  the  minuend. 

3°.  If  two  numbers  are  equally  increased,  their  difference  is 
not  altered. 

15.  From  3427  subtract  1235.  Ans.  2192. 

16.  A  has  8268  more  than  B  and  $150  less  than  C,  who  has 
$4580;  D  has  as  much  as  A  and  B  together;  how  much 
hasD? 

8.  When  the  Sum  and  Difference  of  Two  Numbers  are  given,  to 
find  the  Numbers. 

17.  The  sum  of  two  numbers  is  283,  and  their  difference  is 
35  ;  what  are  the  numbers  ? 

Analysis. — The  difference  subtracted  from  the  sum  will  leave  twice 
the  smaller  number,  and  283-35  =  248 ;  half  of  248  is  124.  the  less  num- 
ber. Again,  the  difference  added  to  the  less  must  be  equal  to  the  greater 
number,  and  124  +  35  =  159,  the  greater  number.     Hence,  the 

Koxe. — From  the  sum  subtract  the  difference ;  half  the 
remainder  will  be  the  less  number. 

TJie  difference  added  to  the  less  will  be  the  greater 
number. 


10  Short  Methods  in  Multiplication. 

18.  The  whole  number  of  votes  cast  for  the  two  candidates  at 
an  election  was  15564,  and  the  successful  candidate  was  elected 
by  a  majority  of  1708  ;  how  many  votes  did  each  receive  ? 

19.  A  lady  paid  $350  for  her  watch  and  chain  ;  the  former 
being  valued  $52  higher  than  the  latter ;  what  was  the  price 
of  each  ? 

20.  A  and  B  found  a  pocket-book,  and  returning  it  to  the 
owner,  received  a  reward  of  $500,  of  which  A  took  $138  more 
than  B ;  what  was  the  share  of  each  ? 

21.  The  sum  of  two  numbers  is  4487,  and  the  greater  is  653 
more  than  the  less ;  what  are  the  numbers  ? 

9.  The  Complement  of  a  number  is  the  difference  between 
the  number  and  the  next  higher  order. 

Thus,  2  is  the  complement  of  8,  also  of  98 ;  for  10—8  =  2,  and 
100-98  =  2. 

22.  What  is  the  complement  of  87  ?     Of  125  ?    Of  3284  ? 

23.  By  how  much  does  the  sum  of  6  and  4  exceed  their 
difference  ? 

24.  By  how  much  does  their  complement  exceed  their  dif- 
ference ? 

25.  Victoria  was  bom  in  1819,  the  Prince  of  Wales  in  1841 ; 
how  old  was  each  in  1882  ? 

26.  A  poor-house  had  133  inmates,  consisting  of  infirm  and 
able-bodied  70  ;  able-bodied  and  children  105  ;  children  and 
officers  63  ;  officers  5  ;  what  number  of  each  class  ? 

27.  A  basket  held  oranges,  nuts,  and  eggs  ;  in  all  1769  arti- 
cles; there  were  1696  oranges  and  nuts,  and  1262  nuts  and 
eggs  ;  how  many  more  nuts  were  there  than  oranges  ? 


Short  Methods  in  Multiplication.  n 


SHORT     METHODS     IN     MULTIPLICATION. 

10.  Peikciples. — 1°.  The  multiplicand  may  be  either  ab- 
stract or  concrete. 

£°.  TJie  multiplier  must  be  considered  an  abstract  number. 

3°.  The  multiplicand  and  product  are  like  numbers. 

4°.  TJie  product  is  the  same  in  whatever  order  the  factors  are 
taken. 

11.  To  multiply  by  I  with  a  significant  figure  annexed. 

1.  If  one  city  lot  costs  $3245,  what  will  17  lots  cost  ? 

Explanation.— Multiply  the  multiplicand  by  the  operation. 
7  units,  and  setting  each  figure  of  the  product  one  place  oZ<kO  X  1  ( 
to  the  right  of  the  order  multiplied,  add  the  partial         22715 

product  to  the  multiplicand.     The  result  is,$55165.  $55165    Ans. 

Note. — This  method  may  be  applied  when  the  multiplier  has  one  or 
more  ciphers  between  the  two  figures,  by  writing  the  product  two  or  more 
places  to  the  right.     (Ex.  6.) 

2.  78465  x  16.  4.     84769  x  17. 

3.  86794  x  18.  5.     79876  x  19. 

6.  Multiply  4584  by  106.      Ans.  485904. 

7.  Multiply  64358  by  108. 

12.  To  multiply  by  I  with  any  significant  figure  prefixed  to  it. 

8.  Multiply  6347  by  41. 

6347  x  41 
Explanation.— Multiply  by  the  tens  and  set  the      25388 

first  product  figure  in  tens  place,  etc.  

*       F  260227,  Ans. 

9.  63758  x  71.         11.  74656  x  81. 
10.  85459  x  61.         12.  87435  x  91. 

13.  73648  x  601.         Ans.   44262448. 

14.  Multiply  84325  by  801. 


12  Short  Methods  in  Multiplication. 

13.  To  multiply  by  the    actors  of  a  number. 

15.  What  will  21  writing-desks  cost  at  $72  apiece  ? 

$72 
Explanation.— The  factors  of  21  are  7  and  3.     As  7 

1  desk  costs  $72,  7  desks  will  cost  7  times  $72,  or  $504  ;  -    ~ 

and  21  desks  will  cost  3  times  as  much  as  7  desks,  or 

504  x  3  =  $1512,  Ansi  3 

$1512,  Ans. 

16.  Multiply  7389  by  63.  17.   Multiply  8479  by  84. 

14.  Moving  a  figure  one  place  .to  the  left,  or  annexing  a 
cipher,  multiplies  a  number  by  10  ;  moving  it  two  places,  or 
annexing  two  ciphers,  multiplies  by  100,  etc. 

18.  Multiply  276  by  100.         20.  Multiply  8760  by  2000. 

19.  Multiply  3458  by  1000.     21.  Multiply  3897  by  32000. 

15.  If  a  number  having  two  figures  is  multiplied  by  11,  the 
product  will  be  the  first  figure  of  the  number,  the  sum  of  the 
two  figures,  and  the  last  figure. 

Thus,  43  x  11  =  473,  or  4,  (4  +  3),  and  3. 

Note. — If  the  sum  of  the  two  figures  exceeds  9,  the  first  or  left-hand 
figure  must  be  increased  by  1.     Thus,  48  x  11  =  528. 

22.  Multiply  45  by  11.  23.  Multiply  67  by  11. 

16.  To  multiply  by  9,  99,  or  any  number  of  9's. 

24.  What  is  the  product  of  2736  multiplied  by  99  ? 

Explanation.— Annexing    two  ciphers  operation. 

to  the  multiplicand,  multiplies  it  by  100;  273600     Prod,  by  100. 

but  99  is  1  less  than  100,  and  subtracting  2736            "           1. 
the  multiplicand  from  the  result  will  give 

the  true  product.     Hence,  the  270864                    99. 

Rule. — Annex  as  many  ciphers  to  the  multiplicand 
as  there  are  9's '  in  the  multiplier,  and  from  the  result 
subtract  the  multiplicand. 

25.  Multiply  62743  by  999.     26.  Multiply  843625  by  9999. 


Short  Methods  in  Multiplication.  13 

17.  To  multiply  by  any  number  which  ends  with  9. 

27.  Multiply  67  by  49. 

Explanation. — The  next  number  higher  than  49  operation. 

is  50.     Multiplying  the  multiplicand  by  5  and  annex-  67  X  50  =  3350 

ing  one  cipher,  the  product  is  3850.     But  49  is  1  less  67  X  1     =       67 
than  50,  and  subtracting  once  the  multiplicand  from 

the  result  gives  the  true  product.  ^ns.   3283 

28.  Multiply  73  by  699. 

Solution.— The  next  number  above  699  is  700,  and  (73x700)-73 
=  51027,  Ans.     Hence,  the 

Rule. — Multiply  by  the  next  higher  number,  and  from 
the  result  subtract  tlte  multiplicand. 

29.  Multiply  642  by  39.  31.   Multiply  423  by  599. 

30.  Multiply  724  by  79.  32.  Multiply  648  by  499. 

18.  To  multiply  by  any  number  that  is  a  little  less  or  a  little 
greater  than  100,  1000,  etc. 

33.  What  is  the  product  of  53172  multiplied  by  993  ? 

Explanation. — The  complement  of  operation. 

993  is  7.     Annexing  3  ciphers  to  the  53172  X  1000  =  53172000 

multiplicand  gives  the  product  by  1000,  53172  X  7          =       372204 
and  subtracting  7  times  the  multiplicand 

from  the  result  gives  the  true  product.  Ans*    ^7yJ79b 

34.  Multiply  63147  by  108. 

Explanation. — The  excess  of  the  mul-  operation. 

tiplier  above  100  is  8.    Therefore  annexing  63147  X  100  =  6314700 

2  ciphers  to  the  multiplicand,   and  adding       63147x8       5051 7P 

to  the  result  its  product  by  8,  gives  the  true  

product.     Hence,  the  Ans.   6819876 

Ktjle.—  Assume  100,  1000,  etc.,  as  the  multiplier ;  this 
product  plus  or  minus  the  product  of  the  multiplicand 
by  the  difference  between  the  true  and  assumed  mul- 
tiplier, will  be  the  true  product. 

35.  56836x96.  37.  915236x9907. 

36.  864532x995.         38,  520316x9904, 


14  Short  Methods  in  Multiplication. 

19.    When  one  part  of  the  multiplier  is  a  factor  of  the  other  part. 

39.  Multiply  436  by  248. 


OPERATION 

436 

Analysis. — Since  8  is  a  factor  of  24,  the  other  fac-  248 

tor  of  which  is  3,  the  product  by  24  will  be  3  times 
the  product  by  8.  The  partial  product  by  8  is  3488, 
and  3488  x  3  =  10464. 


3488 
10464 


40.  Required  the  product  of  6453  by  742. 

Analysis — Since  7  is  a  factor  of  42,  the  other 
factor  of  which  is  6,  the  partial  product  of  7,  multi- 
plied by  C,  equals  the  product  by  42.  The  partial 
product  by  7  is  45171,  the  first  figure  of  which  being 
hundreds,  is  placed  under  the  multiplying  figure. 
(Art.  4, 1°.)  This  partial  product  multiplied  by  6  gives 
the  product  by  42.  The  sum  of  the  two  results  is  the 
true  product.     Hence,  the 


108128,  Ans. 

OPERATION. 

6453 

742 
x6 


45171 

271026 
4788126,  A  ns. 


Rule. — Multiply  by  the  part  of  the  multiplier  which 
is  a  factor  of  the  other  part,  and  this  result  by  the  other 
factor,  setting  the  first  figure  of  each  partial  product 
under  the  right-hand  figure  of  the  part  of  the  multi- 
plier which  produced  it.  TJie  sum  of  the  partial  prod- 
ucts will  be  the  true  product.     (Art.  10,  4°.) 

Note. — When  the  multiplier  has  figures  which  are  not  factors  of 
another  part,  multiply  by  them  in  the  usual  way. 


41.  Multiply  4378  by  428. 

42.  Multiply  6253  by  357. 


43.  Multiply  38674  by  856. 

44.  Multiply  63942  by  639. 


20.   To  multiply  by  two  op  more  figures,  without  setting   down 
the  partial  products. 


45.  Multiply  68  by  43. 

Explanation. — The  product  of  units  (3x8)  —  24,  or 
2  tens  and  4  units.  The  product  of  tens  (3x6  tens)  =  18 
tens,  and  (4  tens  x  8)  =  32  tens.  Now  18  +  32  =  50  tens, 
and  2  to  carry  make  52  tens,  or  5  hundred  and  2  tens. 
Set  the  2  in  tens  place.  Again,  (4  tens  x  6  tens)  =  24 
hundreds   and   5   are  29  hundreds,   or    2   thousands    and 


OPERATION. 

68 
43 


Ans.  2924 

)    hundreds, 

which  aro  written  in  their  proper  places  (Art,  4,  1°.)     The  product  is 
2924. 


Short  Methods  in  Multiplication. 


15 


46.   Multiply  357  by  245. 

Explanation. — The  product  of  the  units  is  35.     Set        operation. 
down  the  units  and  carry  tens.     The  product  of  tens  is 
(5  x  5) +  (7  x  4) +  3,  (carried)  =  56  tens,  or  5  hundreds  and 
6  tens.     Next  the  product  of  hundreds  is  (3  x  5)  +  (5  x  4)  + 
(7  x  2) +  5  =  54  hundreds,  or  5  thousands  and  4  hundreds. 
Again,  the  product  of  thousands  is  (3  x  4)  +  (5  x  2)  +  5  =  27 
thousands,  or  2  ten-thousands  and  7  thousands.     Finally  the  product  of 
ten-thousands  is  (3  x  2) +  2  =  8  ten -thousands.      The  result  87465  is  the 
product.     Hence,  the 


357 

245 

Ans.   874G5 


Eule. — I.  Multiply  the  units,  setting  down  the  result 
and  carrying  as  usual. 

II.  Multiplij  the  orders  which  produce  tens,  and  add- 
ing the  tens  carried,  set  down  the  result  as  before. 

III.  Proceed  in  this  manner  till  all  the  orders  of  the 
multiplicand  are  multiplied  by  each  order  of  the  mul- 
tiplier. 

Note. — With  practice  the  products  may  be  written  without  placing 
the  numbers  under  each  other,  thus  saving  time  in  entering  sales,  etc. 

47.   What  is  the  product  of  23456789  into  54321  ? 

ANALYTIC  SOLUTION. 


2x5 


2x4 
3x5 

2x3 
3x4 
4x5 

2x2 
3x3 
4x4 
5x5 

2x1 
3x2 
4x3 
5x4 
6x5 

3x1 

4x2 
5x3 
6x4 

7x5 

4x1 
5x2 
6x3 
7x4 
8x5 

5x1 
6x2 
7x3 
8x4 
9x5 

6x1 
7x2 
8x3 
9x4 

7x1 
8x2 
9x3 

8x1 
9x2 

9x1 


12 


1 


9 


0 


2 


6 


9 


Note. — In  the  solution  above,  the  multiplications  which  produce  the 
order    are    placed    in  the  same  column,  that  the  results  may  be 
readily  seen. 


48.  Multiply  87  by  54. 

49.  Multiply  256  by  85. 


50.  Multiply  563  by  325. 

51.  Multiply  3754  by  537. 


16  Contractions  in  Division, 


General    Principles    of    Division. 


21.  1°.  Multiplying  the 
dividend,  or  dividing  the 
divisor,  multiplies  the  quo- 
tient. 


Thus,   24-^-4  =  6, 

Then,  (24x2)-j-4  =  6x2, 

And,    24-=- (4-^-2)  =  6x2. 


2°.  Dividing  the  dividend,  1  rpilug  (24-^-2)— 4  =  6—2 
or  multiplying  the  divisor,  \  An^  24-j-(4x2)  =6-5-2! 
divides  the  quotient.  J 

3°.  Multiplying  or  dividing  ~1    Thug    (24^-2)-*-(4— 2)  =  6 

both    by    the    same    number,   [  And  '  (u  '       \_     ^  =  ^ 
does  not  chatige  the  quotient.      J 

Ji°.    When  the  divisor  and  dividend  are  like  numbers,  the 
quotient  is  an  abstract  number. 

5°.    When  the  divisor  is  an  abstract  nun^er,  the  quotient  and 
dividend  are  like  numbers. 

6°.   The  product  of  the  divisor  and  quotient  is  equal  to  the 
dividend. 

CONTRACTIONS     IN    DIVISION. 
22.   To  divide  by  5,  25,  or  125. 

1.  Divide  678  by  5. 

Analysis.— By  Prin.  3°,  5  is  contained  in  678,  operation. 

as  many  times  as  10  {twice  5)  is  contained  in  twice  5    )    678 

678.     Thus,  678x2  =  1356,  and  1356 -i-10  =  135  £            2 

and  6  over;  cutting  off  one  figure  divides  by  10.  — 

The  true  remainder  is  6-r-2  =  3,  which  placed  over  M^  )  loo|o 

the  true  divisor  5  (10-^-2)  becomes  f.  Ans.    135,  3  rem. 

2.  Eequired  the  quotient  of  4364  divided  by  25. 

Analysis. — Reasoning  as  before,  25  is  con-  operation. 

tained  in  4364  as  many  times  as  100  (25  x  4)  is  25    )    4364 

contained  in  4  times  4364,  or  17456.     Cutting  off  4               4 

2  figures  from  the  right  divides  by  100.     The  -\iyA\7r 

figures  cut  off  divided  by  4  gives  a  true  remain-  -M*-^  )  174|oo 

der  of  14,  or  |f     Hence,  the  Ans.    174,  14  rem. 


Contractions  in  Division.  17 

Eule. — I.  To  divide  by  5. — Multiply  the  dividend  by  2 
and  cat  off  one  figure. 

II.  To  divide  by  25. — Multiply  the  dividend  by  4  atid 
cut  off  two  figures. 

III.  To  divide  by  125.     Multiply  by  8  and  cut  off  three 
figures.  # 

Notes. — 1.  The  true  remainder  is  found  by  dividing  the  figures  cut  off 
by  the  number  used  as  the  multiplier. 

2.  The  same  principle  applies  to  any  power  of  5,  the  multiplier  being  a 
like  power  of  2. 

3.  Divide  240653  by  25.  6.  Divide  820345  by  625. 

4.  Divide  963438  by  125.  7.  Divide  579600  by  125. 

5.  Divide  44800  by  25.  8.  Divide  8065227  by  3125. 

23.   To  divide  when  all  the  figures  of  the  divisor,  except  the  first 
on  the  left,  can  be  changed  to  ciphers. 

9.  Divide  35273  by  15. 

Analysis.— The  divisor  15  is  changed  to  30  by  operation. 

multiplying  it  by  2  ;  the  dividend  being  also  niulti-  15  )  35273 

plied  by   2,  the  quotient   is   not   altered.      (Prin.  2              2 

3°.)    Cutting  off  the  cipher  and  dividing  by   3,  SiO  ^7054lf 

there  is  1  remainder,  which  prefixed  to  the  6  cut  off  '     I L_ 

makes  16.     This  divided  by  2  is  the  true  remainder.  Quot.    2351,  8  rem. 

10.  What  is  the  quotient  of  42653  divided  by  75  ? 

Explanation.— Multiplying  by  4,  cutting  75   )  42653 

off  two  figures  and  dividing  as  before,  there  is  4.  4. 

a  remainder  2,  which  prefixed  to  the  figures 
cut  off  gives  212  ;  this  divided  by  4  makes  53, 


3|00)1706|12 


the  true  remainder.     Hence,  the  568,  53   rem. 

Rule. — Multiply  both  the  divisor  and  dividend  by 
such  a  number  as  will  change  all  the  figures  of  the 
divisor  into  ciphers  except  the  first ;  then  divide  as 
usual. 

Note. — If  a  remainder  occurs,  it  must  be  annexed  to  the  figure  cut  off, 
and  this  number,  divided  by  the  multiplier  used,  is  the  true  remainder. 

11.  Divide  38643  by  35.  13.   Divide  624395  by  75. 

12.  Divide  406891  by  45.  14.   Divide  2345062  by  175. 

2 


18  Factoring, 


DIVISIBILITY    OF    NUMBERS. 

24.  An  Exact  Divisor  or  Measure  of  a  number  is  one  which 
will  divide  it  without  a  remainder. 

One  number  is  said  to  be  divisible  by  another  when  there 
is  no  remainder. 

All  numbers  are  divisible 

1°.  By  2,  which  end  with  a  cipher,  or  a  digit  divisible  by  2. 

2°.  By  3,  when  the  sum  of  the  digits  is  divisible  by  3. 

3°.  By  4,  when  the  number  expressed  by  the  two  right-hand 
figures  is  divisible  by  4. 

Jf°.  By  5,  which  end  with  a  cipher  or  5. 

5°.  By  6,  when  divisible  by  2  and  3. 

6°.  By  8,  when  the  three  right-hand  figures  are  ciphers,  or 
when  the  number  expressed  by  them  is  divisible  by  8. 

7°.  By  9,  when  the  sum  of  the  digits  is  divisible  by  9. 

Notes. — 1.  This  principle  of  the  number  9  affords  a  concise  method  of 
proving  Multiplication  and  Division.     (See  Appendix,  Art.  699.) 

2.  The  preceding  is  not  a  necessary  but  an  incidental  property  of  the 
number  9.  It  arises  from  the  Jaw  of  increase  in  the  decimal  notation.  If 
the  radix  of  the  system  were  8,  it  would  belong  to  7 ;  if  the  radix  were  12, 
it  would  belong  to  11 ;  and  universally,  it  belongs  to  the  number  that  is 
one  less  thnn  the  radix  of  tbe  system  of  notation. 

FACTORING. 

25.  The  Factors  of  a  number  are  the  numbers  whose 
product  is  equal  to  that  number.    Thus,  6  and  9  are  factors  of  54. 

26.  A  Composite  Number  is  a  product  of  two  or  more  factors. 

27.  A  Prime  Factor  is  a  prime  number  used  as  a  factor. 

28.  A  Common  Factor  is  an  exact  divisor  of  two  or  more 
numbers. 

Note.— Numbers  are  Prime  to  each,  Qther,  which  have  no  common 
divisor  greater  than  1. 


Factoring.  19 

29.  Factoring  a  number  is  separating  it  into  factors. 

Note. — It  is  not  customary  to  consider  the  unit  1  and  the  number 
itself  as  factors  ;  if  they  were,  all  numbers  would  be  composite.    (Art.  26.) 

30.  Principles. — 1°.  If  one  number  is  a  factor  of  another, 
the  former  is  also  a  factor  of  any  Product  or  Multiple  of  the 
latter. 

2°.  A  factor  common  to  two  or  more  numbers,  is  also  a  factor 
of  their  Sum,  their  Difference,  and  their  Product. 

3°.  Every  composite  number  is  divisible  by  each  of  its  Prime 
factors  ;  and  by  the  Product  of  any  tivo  or  more  of  them. 

31.  To  find  the  Prime  Factors  of  a  number, 
l.  What  are  the  prime  factors  of  2780  ? 

Explanation. — Any  prime  number  operation. 

which  will  exactly  divide  a'  given  num-       2 
ber  is  a  prime  factor  of  it.     The  prime 
numbers  2,  2,  and  5,  exactly  divide  the 
gfiven  number  and  the  successive  quo-       5 
tients.       The   last   quotient,    139,  is   a 
prime  number,  which  with  the  several 
divisors  are  the  prime  factors  required.     For,  139  x  2  x  2  x  5  =  2780. 
Hence,  the 


2780      Given  Number. 
1390      1st  Quotient. 
695      2d 


139     3d 


Rule. — Divide  the  given  number  by  any  prime  factor ; 
then  divide  this  quotient  by  another  prime  factor ;  and 
so  on  until  the  quotient  obtained  is  a  prime  number. 
The  several  divisors,  with  the  last  quotient,  are  the  prime 
factors  required. 

2.  What  is  the  only  even  prime  number  ?  When  are  two 
numbers  prime  to  each  other  ? 

Find  the  prime  f  J^tors  of 

3.  286.  5.     2460.  7.     3225.  9.     2572. 

4.  48831.  6.     2810.  8.     3840.  10.     8964. 


20  Factoring. 

32.  To  find  the  Prime  Factors  common  to  two  or  more  numbers. 

11.  What  are  the  prime  factors  common  to  264,  84,  and  450  ? 

Explanation.— Since  the  prime  numbers  2,  ^  )   264,      84,      450 

2,  and  3,  divide  the  given  numbers  and  succes-  2   )   132       42       225 

sive  quotients,  and  the  last  quotients  are  prime 

to  each  other,  the  several  divisors  are  the  prime  ^   )      66,      21,      225 

factors  required.     Hence,  the  22          7          75 

Bule. — Divide  the  given  numbers  by  any  common 
prime  factor,  and  the  quotients  thence  arising  in  like 
manner,  till  they  have  no  common  factor ;  the  several 
divisors  will  be  the  prime  factors  required. 

12.  Find  the  prime  factors  common  to  326,  452,  and  450. 

13.  240,  96,  684.     14.     264,  640,  456.     15.     325,  650,  875. 

CANCELLATION. 

33.  Cancellation  is  the  method  of  shortening  operations  hy 
rejecting  equal  factors  from  the  divisor  and  dividend. 

The  Sign  of  Cancellation  is  an  oblique  mark  drawn  across 
the  face  of  a  figure ;  as,  $,  0,  $,  etc. 

34.  Principles.— 1°.  Cancelling  a  factor  of  a  number  di- 
vides the  number  by  that  factor. 

2°.  Cancelling  equal  factors  of  the  divisor  and  dividend  does 
not  change  the  quotient.     (Art.  21,  3°.) 

35.  Cancellation  may  be  applied  to  all  examples  in  which 
the  divisor  and  dividend  have  one  or  more  common  factors. 

l.  Divide  the  product  of  18  x  16  x  28  by  the  product  of 
12  x  7  x  14. 

SOLUTION. 


3                         X 

X$xl6xn       3x16 
XtxlxW       7 

Or, 
=  6-|,  Ans. 

7 
U 

1$  3 

16 

& 

7 

48  =  6|,  Ans 

Greatest  Common  Divisor.  21 

Explanation. — The  division  may  be  represented  in  the  form  of  a  frac- 
tion, or  with  the  dividend  on  the  right  and  ihe  divisor  on  the  left  of  a 
vertical    line.       Cancelling    the    factors    common    to   both,   it    becomes 

— — —  =  6f.     Hence,  the 

Eule.—  Cancel  the  factors  common  to  the  divisor  and 
dividend,  and  divide  the  product  of  those  remaining  in 
the  dividend  by  the  product  of  those  remaining  in  the 
divisor. 

Note. — When  a  factor  cancelled  is  equal  to  the  number  itself,  the  unit 
1  always  remains.  If  the  1  is  in  the  dividend  it  must  be  retained ;  if  in 
the  divisor,  it  may  be  disregarded. 

2.  Multiply  74  x  12  by  14  x  6,  and  divide  the  product  by 
28x72x24. 

3.  Divide  112  x  27  x  163  by  54  x  63  x  89. 

4.  128  x  16  x72-f-44x  32x18. 

5.  135  x  12  x  29-^27  x  18  x  154. 

6.  45x63x144^72x24. 

7.  28x42x96^-7x21x12. 

8.  If  24  pieces  of  cloth,  containing  32  yards  each,  cost  $384, 
what  will  48  yards  cost  ? 

9.  Bought  48  tons  of  coal  at  $9  a  ton  ;  how  many  barrels  of 
flour,  at  $12  a  barrel,  will  pay  for  it  ? 

10.  If  26  bushels  of  wheat  make  6  barrels  of  flour,  how  many 
bushels  will  be  required  to  make  156  barrels  ? 

11.  If  500  copies  of  a  book  of  210  pages  require  12  reams  of 
paper,  how  much  will  1200  copies  of  a  book  of  280  pages 
require  ? 

12.  If  9  men  cut  150  acres  of  grass  in  18  days,  how  many 
men  will  do  the  same  work  in  27  days  ? 

GREATEST     COMMON     DIVISOR. 

36.  A  Common  Divisor  or  Measure  is  a  number  that  will 
divide  two  or  more  numbers  without  a  remainder. 

37.  The  Greatest  Common  Divisor  or  Measure  of  two  or 
more  numbers  is  the  greatest  number  that  will  divide  each  of 
them  without  a  remainder. 

Thus,  the  greatest  common  divisor  of  18  and  30  is  6. 

Note. — The  letters  a.  c,  d.  stand  for  greatest  common  divisor. 


22  Greatest  Common  Divisor, 

38.  Principles. — 1°.  An  exact  divisor  of  a  number  is  a 
divisor  of  any  multiple  of  that  number. 

2°.  A  common  divisor  of  two  numbers  is  a  divisor  of  their 
sum  and  of  their  difference. 

3°.  The  greatest  common  divisor  of  two  or  more  numbers  is 
the  product  of  all  their  common  prime  factors. 

39.  To  find  the  Greatest. Common  Divisor  by  Factoring. 

1.  What  is  the  g.  c.  d.  of  84,  96,  276  ? 

OPERATION. 

2  )  84,     96,     276  84  =  2x2x3x7 

2  )  42,     487~l38  96  =  2x2x3x8 

3  )  21,     24,       69  276  =  2  x  2  x  3  x  23 

7,       8,       23       Ans.  2  x  2  x  3  =  12,  g.  c.  d.     Hence,  the 

Kule. — Separate  the  numbers  into  their  prime  factors ; 
the  product  of  those  that  are  common  to  each  is  the 
greatest  common  divisor. 

What  is  the  greatest  common  divisor  of 

2.  144  and  288.         4.  46  and  322.         6.  475  and  589. 

3.  112  and  254.         5.  84  and  268.         7.  516  and  898. 

8.  What  is  the  greatest  length  of  boards  that  may  be  used 
without  cutting  to  fence  two  sides  of  a  lot,  one  80  ft.,  the 
other  144  ft.  long  ? 

9.  The  g.  c.  d.  of  896,  254  ?  10.   Of  324,  816  ? 

40.  To  find  the  g.  c.  d.  by  continued  division, 
li.  What  is  the  g.  c.  d.  of  96  and  876  ? 


OPERATION. 


Explanation. — When  the   greater    number  is       qp  x  „„„  ,  ~ 
divided  by  the  less,*the  quotient  is  9  and  12  remain-  '  ^ 

der.     The  divisor  96,  divided  by  the  remainder  12, 
has  no  remainder  ;  therefore,  12  is  tlie  greatest  com-  12  )  96  ( 

mon  divisor.    Hence,  the  9@ 


Common  Multiples.  23 

Rule. — Divide  the  greater  number  by  the  less;  then 
divide  the  first  divisor  by  the  first  remainder,  and  so 
on,  until  nothing  remains ;  the  last  divisor  will  be  the 
greatest  coimnon  divisor. 

If  there  are  more  than  two  numbers,  find  the  greatest 
common  divisor  of  two  of  them;  then  of  this  divisor 
and  a  third  number,  and  so  on,  until  all  the  numbers 
have  been  taken. 

Note. — The  greatest  common  divisor  of  two  or  more  'prime  numbers, 
or  numbers  'prime  to  each  other  is  1.     (Art.  28,  N.) 

12.  A  man  has  3  farms  containing  respectively  128,  236,  and 
344  acres  ;  what  is  the  largest  number  of  acres  that  he  can  put 
into  fields  of  equal  size  in  all  the  farms  ? 

13.  What  is  the  greatest  width  of  matting  that  may  be  used 
without  cutting,  to  cover  the  floors*  of  3  rooms  of  15,  18,  and 
24  feet  wide  respectively  ? 

14.  The  four  sides  of  a  garden  are  168,  280,  182,  and  252  ft. 
respectively ;  what  is  the  greatest  length  of  boards  that  may 
be  used  in  fencing  it  without  cutting  any  of  them  ? 

15.  A  merchant  wished  to  cut  equal  dress-patterns  from 
3  pieces  of  silk  containing  respectively  48,  32,  and  64  yds. ; 
what  is  the  greatest  length  of  the  patterns  ? 


COMMON    MULTIPLES. 

41.  A  Multiple  of  a  number  is  one  which  is  exactly  divisi- 
ble by  that  number. 

Thus,  12  is  a  multiple  of  4 ;  18  of  6. 

42.  A  Common  Multiple  is  a  number  that  is  exactly  divisible 
by  two  or  more  numbers. 

Thus,  18  is  a  common  multiple  of  2,  3,  6,  and  9. 

43.  The  Least  Common  Multiple  (I.  c.  fit.)  of  two  or  more 
numbers,  is  the  least  number  exactly  divisible  by  each  of  them. 

Thus,  15  is  the  least  common  multiple  of  3  and  5. 


2  )  20, 

24, 

36 

2  )  10, 

12, 

18 

3  )    5, 

6, 

9 

5, 

2, 

3 

24  Common  Multiples. 

44.  Principles. — i°.  A  multiple  of  a  number  must  contain 
all  the  prime  factors  of  that  number. 

2°.  A  common  multiple  of  two  or  more  numbers  must  contain 
all  the  prime  factors  of  each  of  the  given  numbers. 

3°.  Tlie  least  common  multiple  of  two  or  more  numbers  is  the 
least  number  which  contains  all  their  prime  factors,  each  factor 
being  taken  the  greatest  number  of  times  it  occurs  in  either  of 
the  given  numbers, 

45.  To  find  the  Least  Common  Multiple  of  two  or  more  numbers. 

1.  What  is  the  I.  c.  m.  of  20,  24,  and  36  ? 

Explanation.  —A rrange  the 
numbers  in  a  line  and  divide  by 
any  prime  number,  as  2,  that  will 
exactly  divide  two  or  more  of  them, 
setting  the  quotients  and  undivided 
numbers  below.  Continue  dividing 
till  no  two  of  the  numbers  have  a 
common  factor.  The  continued  2x2x3x5x2x3  =  360,  A ns. 
product  of  the  divisors  2,  2,  3,  and 

the  prime  numbers  5,    2,    and  3,  is  360,   the  least   common  multiple 
required.     Hence,  the 

Rule. —  Write  the  numbers  in  a  line,  and  divide  by 
any  prime  number  that  will  divide  two  or  more  of  them 
without  a  remainder,  placing  the  quotients  and,  undi- 
vided numbers  in  a  line  below. 

Repeat  the  operation  till  no  two  numbers  are  divisible 
by  any  number  greater  than  1.  The  continued  product 
of  the  divisors  and  numbers  in  the  last  line  is  the 
answer. 

Notes.— 1.  The  operation  may  often  be  shortened  by  cancelling  any 
number  which  is  a  factor  of  another  number  in  the  same  line. 

2.  When  the  given  numbers  are  prime  or  prime  to  each  other,  their  con- 
tinued product  will  be  the  least  common  multiple. 

3.  The  I.  c.  m.  of  fractions  equals  the  1.  c.  m.  of  the  numerators 
divided  by  the  a.  c.  d.  of  the  denominators.  The  result  may  be  expressed^ 
as  a  fraction,  a  mixed  number,  or  an  integer,  as  the  case  may  be.  Thus, 
the  1.  <',  m.  of  |,  f ,  rnd  £  is  the  integer  12,  the  denominators  being  prime 
to  each  other. 


Common  Multiples.  25 

2.  What  is  the  I.  c.  m.  of  21,  35,  42  ? 

3.  21,  36,  50,  64  ?  7.   189,  153,  144  ? 

4.  48,  98,  21,  27  ?  8.  3150,  2310  ? 

5.  16,  40,  96,  105?  9.  43T00,  9430? 

6.  25,  36,  33,  12  ?  10.   729,  336,  1836  ? 
n.  Find  the  I.  c.  m.  of  the  9  digits. 

12.  Of  the  even  numbers  from  1  to  21. 

13.  Of  what  is  the  I,  c.  fit.  of  several  numbers  the  product  ? 

14.  Find  the  least  common  multiple  of  §,  J,  f ,  and  f . 

15.  A  bookseller  ordered  boxes  in  which  to  pack  books  3,  4, 
and  6  inches  long ;  what  is  the  shortest  box  in  which  these 
books  could  exactly  fill  the  space  ? 

16.  What  is  the  least  number  of  peaches  that  can  be  exactly 
divided  among  3  classes  of  children  containing  15,  18,  and  24 
pupils  respectively? 

17.  Find  the  least  number  of  weeks  in  which  a  man  who 
earns  $18  a  week  can  earn  an  exact  number  of  double- eagles. 

18.  Find  the  I.  c.  m.  of  f ,  &,  and  |f 

19.  The  price  of  Histories  is  44  cents,  of  Arithmetics  32 
cents,  and  of  Grammars  36  cents  each  ;  what  is  the  least  equal 
sum  a  teacher  could  expend  on  each?  How  many  of  each 
could  he  buy  ? 


^eights  and    Measures 


LINEAR    MEASURE. 

46.  A  Measure  is  a  standard  unit  established  by  law  or 
custom,  by  which  the  length,  surface,  capacity,  and  weight  of 
things  are  estimated. 

47.  Linear  Measure  is  used  in  measuring  lines  and  dis- 
tances. 

48.  A  Line  is  that  which  has  length  only. 

Table. 

12  inches  (in.)  =  1  foot,     .  .  .  ft. 

3  feet  =  1  yard,    .  .  .  yd. 

5|  yds.,  or  16|  ft.  =  1  rod,     .  .  .  rd. 

40  rods  =  1  furlong,  .  .  fur. 

320  rods,  or) 

5280  fee.        I  =  *  mi,e'    •  ■  ■  "* 

3  miles  =  1  league,  .  .  I. 

Note. — The  yard  for  common  use  is  divided  into  halves,  quarters, 
eighths,  and  sixteenths.  At  the  U.  S.  Custom  Houses  it  is  divided  into 
tenths  and  hundredths. 

49.  The  Standard  Unit  of  length  in  the  United  States  and 
England  is  the  Yard  of  3  feet. 

Note. — The  Standard  Yard  is  determined  by  the  pendulum,  which 
vibrates  seconds  in  a  vacuum  at  the  level  of  the  sea,  in  the  latitude  of 
London,  and  the  temperature  of  62"  Fahrenheit.  This  pendulum  is 
divided  into  391393  equal  parts,  and  360000  of  these  parts  constitute 
a  yard. 


^  inch 


Square  Measure.  27 

Special     Linear     Measures. 

~     -11*        [  Applied  to  pendulums. 


3^  inch 

i  inch  =  1  size,  applied  to  shoes. 

18  inches  =  1  cubit. 

3.3  feet  s=  1  pace. 

5  paces  =  1  rod. 

6  feet  =1  fathom. 

20  fathoms  s  1  cable  length. 

120  knots,  or 


1.16  statute  miles 


=     1  Nautical  or  Geographical  mile. 


00      geog.,  or         )  j  1  Degree  of  Long,  on  the  Equator,  or 

69.16  statute  miles  (       ~  ( 1  Degree  of  a  Meridian. 
360      degrees  =     Circumference  of  the  Earth. 


SQUARE     MEASURE. 

50.  Square  Measure  is  used  in  measuring  surfaces;  as, 
flooring,  land,  etc. 

51.  A  Surface  is  that  which  has  length  and  breadth  only. 

Table. 

144    square  inches  (sq.  in.)  =  1  square  foot,    .     .     sq.  ft. 

9    square  feet  =  1  square  yard,  .     .     sq.  yd. 

SOI  SQ-  yards,  or  )  j  1  sq.   rod,  perch 

272^  sq.  feet,  )  )      or  pole,  .     .     .     sq.  r. 

160    square  rods  =  1  acre,      .     .     .     .A. 

640    acres  =  1  square  mile,   .     .     sq.  m. 

52.  The  measuring  unit  of  surfaces  is  a  Square,  each  side 
of  which  is  a  linear  unit. 

53.  A  Square  is  a  rectilinear  figure  which  has/o&r  equal 
sides,  and  four  right  angles. 

54.  The  Area  of  a  figure  is  the  quantity  of  surface  it  con- 
tains. 

*  The  progress  of  sailing  vessels  is  determined  by  a  half-mmvte.  glass  and  a  log  line, 
"'hich  is  divided  into  knots,  bearing  the  same  ratio  to  a  mile  that  a  half -minute  has  to 
**\  hour. 


28  Weights  and  Measures. 


SURVEYOR'S     MEASURE. 

55.  Surveyor's  Measure  is  used  in  measuring  land,  etc. 

56.  The  Linear  Unit  commonly  employed  by  surveyors  is 
Guntefs  Chain,  which  is  4  rods  or  60  feet  long,  and  divided 
into  100  links. 

Table. 

7.92  inches  {in.)  —  1  link, J. 

25  links  =  1  rod  or  pole,  .    .     .  r. 

4  rods,  or  100  links  =  1  chain,      .     ...  eh. 

80  chains  =  1  mile m. 

Notes. — 1.  Surveyors  usually  record  distances  in  chains  and  hun- 
dredths of  a  chain.     Thus,  45  ch.  37  1.  is  written  45.37. 

2.  In  measuring  roads,  etc.,  engineers  use  a  chain,  or  measuring  tape, 
100  feet  long,  each  foot  being  divided  into  tenths  and  hundredths. 

57.  The  Measuring  Unit  of  Land  is  the  Acre. 

Table. 


625  sq.  links  =    1  sq.  rod  or  pole,       .     sg.  rd. 

16  sq.  rods  =    1  sq.  chain,     .     .     .     sq.  c. 

10  sq.  chains,  or  )         ., 

-«/v  ,  >  =   1  acre, A. 

160  sq.  rods  \ 

640  acres  =    1  sq.  mile,       .     .     .     sq.  mi. 

Notes. — 1.  The  Rood  of  40  sq.  rods  has  fallen  into  disuse. 
2.  A  Square,  in  Architecture,  is  100  square  feet. 

58.  In  Surveying  Government  Lands  a  parallel  of  latitude 
called  the  Base  Line,  and  a  meridian  called  the  Principal  Meri- 
dian are  first  established.  From  these  other  lines  are  run  at 
right  angles,  six  miles  apart,  which  divide  the  territory  into 
rectangular  tracts  six  miles  square. 

These  tracts  are  called  Townships. 

Since  the  surface  of  the  Earth  is  convex,  all  Meridians 
converge  as  the  latitude  increases.  Hence,  the  Townships  and 
Sections  are  not  exactly  rectangular,  which  creates  a  necessity 
for  occasional  offsets  called  Correction  Lines. 

59.  Townships  are  designated  by  their  number  N.  or  S.  of 
the  base  line. 


Cubic  Meastire. 


29 


60.  A  line  of  townships  running  N.  and  S.  is  called  a 
Range,  and  is  designated  by  its  number  E.  or  W.  of  the  prin- 
cipal meridian.     Thus, 

T.  39  N.,  R.  14  E.  3d  P.  M.,  describes  a  township  in  the  39th  tier  North 
of  base  line,  and  14th  range  East  of  the  3d  A  sectkjn. 

principal  meridian. 


61.  A  Township  is  divided  into 
Sections  each  1  mile  square  and  con- 
tains 640  acres.     Thus, 


1  Sec. 

=  1  mi.  x  1  mi.  =  640  A. 

\  Sec. 

=  1  "     x|"     =320  " 

\  Sec. 

=  1  «     x  i   "     =160  " 

jx  J  Sec. 

.-=  1  "     x  I  "     =     80  " 

\*\  Sec. 

=  1"     x  TV "     =     40  * 

The  sections  are  numbered  commencing 
at  the  N.  E.  corner,  and  running  W.  in 
the  North  tier,  E.  in  the  second,  etc. 

Each  section  is  divided  into  4  quarter 
sections,  called  N.  E.,  S.  E.,  N.  W.,  and 
S.  W.  quarters,  each  containing  160  acres. 

Thus,  S.E.  \,  sec.  10,  T.  39  N.,  R.  14  E. 
3d.,  P.  M.,  is  read,  "  Southeast  quarter  of 
sec.  16,  tier  39  north,  range  14  east  of 
third  principal  meridian." 


1  MILE  SQUARE. 


A  TOWNSHIP. 
N 


W 


6 

5 

4 

3 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

18 

15 

14 

13 

19 

20 

21 

89 

23 

21 

30 

20 

2S 

~7 

26 

25 

31 

32 

33 

34 

35 

36 

6  MILES  SQUARE. 


CUBIC     MEASURE. 

62.  Cubic  Measure  is  used  in  measuring  solids  or  volume. 

63.  A  Solid  is  that  which  has  length,  breadth,  and  thickness  ; 
as,  timber,  boxes  of  goods,  etc. 

64.  A  Cube  is  a  regular  solid  bounded  by  six  equal  squares 
called  its  faces.  Hence,  its  length,  breadth,  and  thickness  are 
equal  to  each  other. 

65.  The  measuring  unit  of  solids  is  a  Cube  the  edge  of 
which  is  a  linear  unit. 


30  Weights  and  Measures. 

Table. 

1728  cubic  inches  {cu.  in.)  =  1  cubic  foot,    .  .  cu.ft. 

27  cubic  feet                      =  1  cubic  yard,   .  .  cu.  yd. 

128  cubic  feet                      =  1  cord  of  wood,  .  C. 

66.  A  Cord  of  wood  is  a  pile  8  ft.  long,  4  ft.  wide,  and  4  ft. 
high;  for  8x4x4  =  128. 

67.  A  Cord  Foot  is  one  foot  in  length  of  such  a  pile  ;  hence, 
1  cord  foot  =  16  cu.  feet;  8  cord  ft.  =  1  cord. 

Special     Cubic     Measures. 

100  cu.  ft.  =  1  register  ton  (shipping.) 

40  cu.  ft.  in  U.  S.,  or,  )        .  ..  .  ■ 
42cu.ft.inEng.  \=  1  fre^ht  ton- 

Note. — A  cu.  foot  of  distilled  water  maximum  density  weighs  62|  lbs. 
avoirdupois. 

LIQUID     MEASURE. 

68.  Liquid  Measure  is  used  in  measuring  milk,  oil, 
wine,  etc. 

Ta  ble. 

4    gills  (gi.)   =   1  pint    .     .  .  pt. 

2    pints  =    1  quart       .  .  qt. 

4    quarts        =    1  gallon,     .  .  gal. 

31 J  gallons      =    1  barrel,     .  .  bar.  or  bbl. 

63    gallons      ==    1  hogshead,  .  hhd. 

69.  The  Standard  Unit  of  Liquid  Measure  is  the  gallon, 
which  contains  231  cubic  inches. 

The  British  Imperial  Gallon  contains  277.274  cu.  inches. 

Notes. — 1.  The  barrel  and  hogshead,  as  units  of  measure,  are  chiefly 
used  in  estimating  the  contents  of  cisterns,  reservoirs,  etc. 

2.  Casks  varying  in  capacity  are  often  used  in  commerce,  called  tierces, 
pipes,  butts,  tuns,  etc.  Their  capacity  is  determined  by  gauging  or 
measurement,  and  the  number  of  gallons  each  contains  is  usually  marked 
upon  it. 

3.  A  Carboy  holding  about  12  gallons,  is  sometimes  used  for  corrosive 
and  other  liquids. 

4.  Beer  Measure  is  practically  obsolete  in  this  country.  The  old  beer 
gallon  contained  282  cubic  inches ;  the  barrel  36  gallons  ;  the  hogshead 
51  gallons. 


Dry  Measivre. 


31 


DRY     MEASURE. 


70.    Dry 

salt,  etc. 


Measure    is    used    in    measuring  grain,   fruity 


Table. 

2  pints  (pt.)  =  1  quart,     . 

8  quarts  =  1  peck, 

4  pecks,  or  32  qts.  =  1  bushel,  . 

36  bushels  =  1  chaldron, 


qt. 
pk. 
bu. 
ch. 


71.  The  Standard  Unit  of  Dry  Measure  is  the  bushel,  which 
contains  2150.42  cu.  inches. 


The  British  Imperial  bushel  contains  2218.192  cu.  inches. 


Notes. — 1.  The  Eng.  Quarter  seen  in,  prices  current,  is  equal  to  8  bu. 
of  70  lb.  each,  or  to  560  lb.  =  \  of  a  long  ton. 

2.  Stricken  or  Even  Measure  is  used  in  measuring  grain,  seeds,  etc., 
the  article  measured  being  scraped  off  level  by  a  straight  instrument 
called  a  strike,  or  strickle. 

3.  Heaped  Measure  is  used  in  measuring  vegetables  and  fruit,  as 
potatoes,  apples,  etc. 

4.  A  heaped  bushel  is  equivalent  to  a  Winchester  bushel,  heaped  in 
the  form  of  a  cone,  the  height  of  which  is  6  inches. 

Four  heaped  measures  are  about  equal  to  five  stricken  measures. 


72.    The  standard  weight,  Avoirdupois,  of  a   Bushel   of  different 
kinds  of  grain  and  seeds,  as  fixed  by  law  in  the  several  States  named. 

Table. 


commodities. 


Wheat 

Indian  Corn 

Oats 

Barley 

Buckwheat 

Rye... 

Clover  Seed 

Timothy  Seed . . . 
Blue  Grass  Seed 

Flax  Seed 

Hemp  Seed 


60  56 
52|56 
32 

50 


1 

i  | 

IN 


60 
5(^52 


|  i 


60  60  60 


50  56 
33 


-   1 

i  1 


60|  60  GO  60  60  60 
66  56  56|  56  52  56 
32  30 
!46 


32  35  30 


48  48 
52  50  48 
56  56  56 


60  64 

45 

14' 

56  5Dj5£ 

44 


60  60 
54  56 

.32 


is 


5C, 


CO  60 
56  56 
861  32 
45  48 
42  42 
56  56 
60  60 
46 
!56 

I 


32  Weights  and  Measures. 

Notes.— 1.  Beans,  peas,  and  potatoes  v.re  usually  estimated  at  60  lb.  to 
the  bu.,  but  the  laws  of  N.  Y.  make  62  lo.  of  Leans  to  a  bushel. 

In  Illinois,  50  lb.  of  common  salt,  or  55  lb.  fine,  are  1  bu.  In  N.  J., 
56  lb.  of  salt  are  1  bu.  In  Ind.,  Ky.,  and  Iowa,  50  lb.  are  1  bu.  In  Penn., 
80  lb.  coarse,  70  lb.  ground,  or  62  lb.  fine  salt  are  1  bu. 

In  Maine,  30  lb.  oats,  and  64  lb.  beets  or  of  rutabaga  turnips  =  1  bu. 

In  New  Hampshire,  30  lb.  of  oats  are  1  bu. 

2.  Grains,  seeds,  and  small  fruit  are  sold  by  the  bushel,  stricken  or 
level  measure. 

Large  fruit,  potatoes,  and  all  coarse  vegetables  by  heaped  measure. 


TROY    WEIGHT. 

73.  Troy  Weight  is  used  in  weighing  gold,  silver,  jewels,  and 
in  philosophical  experiments. 

Table. 

24  grains  (gr.)        =     1  pennyweight,     .    pwt. 
20  pennyweights    =     1  ounce,    .     .     .     .    oz. 
12  ounces  =     1  pound,  .     ...    lb. 

74.  The  Standard  Unit  of  weight  in  the  United  States,  is 
the  Troy  pound,  which  contains  5760  grains  and  is  equal  to 
the  Imperial  Troy  pound  of  England. 

75.  The  Value  of  Diamonds  and  other  jewels  is  estimated 
by  carats,  grains,  and  quarters.     Thus, 

4  quarters     =     1  grain,     .         .    gr. 
4  grains        =     1  carat,      .    .    .    car. 

AVOIRDUPOIS     WEIGHT. 

76.  Avoirdupois  Weight  is  used  in  weighing  coarse  articles; 
as  hay,  cotton,  groceries,  etc.,  and  all  metals  except  gold  and 
silver. 

Table. 

16  ounces  {oz)        =  1     pound,     .    .     .  lb. 

_        j  cental,  or     .     .  ctl. 

^  1  hundredweight,  cwt. 

2000  lb.,  or  20  cwt.    =  1     ton,     .     .     .     .  T. 

Note. — The  long  ton  of  2240  lbs.  is  used  in  calculating  duties,  in 
weighing  coal  at  the  mines,  and  in  a  few  other  cases. 


Apothecaries   Weight  33 

77.    Comparison  of  Avoirdupois  and  Troy  Weight. 

7000    grains  Troy  =  1  lb.  Avoirdupois. 

5760    grains      "  =  1  lb.  Troy. 

437^  grains      "  =  1  oz.  Avoirdupois. 

480    grains      "  =  1  oz.  Troy. 


Special    Avoirdupois 

Weights. 

100 

lbs.  Nails 

=     1  Keg. 

100 

lbs.  Dry  Fish 

=     1  Quintal. 

196 

lbs.  Flour 

=     1  Barrel. 

200 

lbs.  Beef  or  Pork 

=     1  Barrel. 

240 

lbs.  Lime 

=     1  Cask. 

280 

lbs.  Salt,  N.  Y.  Salt  Works 

=     1  Barrel. 

150 

lbs.  Potatoes,  as  freight 

=     1  Barrel. 

6|  lbs.  Crude  or  Refined  Petroleum  =     1  Gallon. 

A  ton  (2000  lbs.)  of  Lehigh  white  ash  coal,  egg  size  =  34|  cu.  ft. 
A  ion  of  white  ash  Schuylkill,  "        =35    cu.  ft. 

A  ton  of  pink,  gray,  and  red  ash,  "         =36    cu.  ft. 

A  ton  of  hay  upon  a  scaffold  measures  about  500  cu.  ft. ;  when  in  a 
mow,  400  cu.  ft. ;  and  in  well-settled  stacks,  10  cu.  yards. 


APOTHECARIES     WEIGHT. 

78.  Apothecaries  Weight  is  used  by  apothecaries  in  mixing 
medicines. 

Table. 

20  grains  (gr.)  =  1  scruple,  .  .  sc,  or  B. 

3  scruples  =  1  dram,    .  .  .  dr.,  or  3 . 

8  drams  =  1  ounce,  .  .  .  oz.t  or  §  . 

12  ounces  =  1  pound,  .  .  .  lb.,  or  lb. 

Notes. — 1.  The  pound,  ounce,  and  grain  are  the  same  as  Troy 
weight.  The  only  difference  between  them  is  in  the  subdivisions  of  the 
ounce. 

2.  Drugs  and  Medicines  are  sold  at  wholesale  by  Avoirdupois 
weight. 

3 


34  Weights  and  Measures. 


APOTHECARIES     FLUID     MEASURE. 

79.  Apothecaries  Fluid  Measure  is  used  in  mixing  liquid 
medicines. 

Table. 

60  minims,  or  drops  (TR.  or  git.)  =  1  fluid  drachm,      .  fl . 

8  fluid  drachms                          =  1  fluid  ounce.    .     .  /§ . 

16  fluid  ounces  =     1  pint 0. 

8  pints                                         =  1  gallon,  ....  Cong. 

Notes.— 1.  Ott.  for  guttoa,  Latin,  signifying  drops  ;  O,iovoctarias,  Latin 
for  one-eighth  ;  and  Cong.,  congiarium,  Latin  for  gallon. 

2.  The  symbols  of  this  measure  precede  the  numbers  to  which  they 
refer.     Thus,  O.  2  "f  §6,  is  2  pints  6  fluid  ounces. 

80.  The  following  approximate  measures,  though  not 
strictly  accurate,  are  often  useful  in  practical  life : 

Table. 

45  drops  of  water,  or  a  common  teaspocnful  =  1  fluid  drachm. 

A  common  tablespoonful  =  -|  fluid  ounce. 

A  small  teacupful,  or  1  gill  =  4  fluid  ounces. 

A  pint  of  pure  water  =  1  pound. 

4  tablespoonful s,  or  a  wine-glass  =  £  gill. 

A  common-sized  tumbler  =  \  pint. 

4  teaspoonfuls  =  1  tablespoonful. 

Abbreviations.—^,  recipe,  or  take;  a,  aa,  equal  quantities;  j,  1; 
ij,  2 ;  ss,  semi,  half;  P,  particula,  little  part ;  P.  aeq.,  equal  parts  ;  q.  p., 
as  much  as  you  please. 


CIRCULAR    MEASURE. 

81.  Circular  Measure  is  used  in  measuring  angles,  latitude, 
longitude,  etc. 

82.  A  Circle  is  a  plane  figure  bounded  by  a  curve  line, 
every  part  of  which  is  equally  distant  from  a  point  within, 
called  the  center. 


Time.  35 

Table. 

60  seconds  (")  =  1  minute,     .     .  '. 

60  minutes  =  1  degree,     .     .  °,  or  deg. 

30  degrees  =  1  sign,     .     .     .  S. 

12  signs,  or  360'  =  1  circumference,  Gir. 

The  Standard  Unit  for  measuring  angles  is  the  Degree. 

83.  A  Degree  is  the  angle  measured  by  the  arc  of  -jj-g-  part 
of  the  circumference  of  a  circle. 

A  degree  at  the  equator,  also  the  average  degree  of  latitude, 
adopted  by  the  U.  S.  Coast  Survey,  is  equal  69.16  miles,  or 
69|  miles,  nearly. 

TIME. 

84.  Time  is  a  measured  portion  of  duration. 

Table. 

60  seconds  (sec.)  =  1  minute,    .  .  rain. 

60  minutes  =  1  hour,   .     .  .  hr. 

24  hours  ==  1  day,     .     .  .  d. 

7  days  --  1  week,  .     .  .  wk. 

365  days  =  1  common  year,  c.  yr. 

366  days  =  1  leap  year,  .  I.  yr. 
12  calendar  months  (mo.)  =  1  civil  year,  .  yr. 

100  years  =     1  century,  .     .     0. 

Note. — In  most  business  transactions  30  days  are  considered  a  month. 

85.  Time  is  naturally  divided  into  days  and  years.  The 
former  are  measured  by  the  revolution  of  the  earth  on  its  axis ; 
the  latter  by  its  revolution  around  the  sun. 

86.  Days  are  divided  into  Apparent  Solar,  Mean  Solar,  and 
Civil  days. 

An  Apparent  Solar  Day  is  the  time  between  the  apparent 
departure  of  the  sun  from  a  given  meridian  and  his  return  to 
it,  and  is  shown  by  sun  dials. 

A  Mean  Solar  Day  is  the  average  length  of  apparent  solar 


36 


Weights  and  Measures. 


days,  and  is  the  Standard  Unit  for  measuring  Time.  It  is 
divided  into  24  equal  parts,  called  hoars,  as  shown  by  a  per- 
fect clock. 

A  Civil  Day  is  the  day  adopted  by  government  for  business 
purposes.  It  begins  and  ends  at  midnight,  and  is  divided  into 
two  part^  of  12  hours  each  ;  the  former  are  designated  A.  M., 
the  latter  p.  m. 

Notes. — 1.  The  difference  between  the  apparent  and  mean  solar  day 
is  called  the  Equation  of  Time,  and  varies  from  16£  min.  to  nothing. 
This  difference  is  owing  to  the  obliquity  of  the  ecliptic,  and  the  unequal 
velocity  of  the  Earth  in  its  orbit. 

2.  The  Astronomical  Day  begins  at  noon  and  is  counted  on  through 
24  hours  to  the  next  noon,  and  corresponds  to  the  apparent  solar  day. 

3.  We  have  seen  that  the  pendulum  which  vibrates  seconds,  is  the 
standard  of  the  English  and  American  measures  of  extension,  capacity, 
and  weight.  But  the  length  of  the  pendulum  is  determined  by  the  mean 
solar  day ;  hence,  the  mean  solar  day  is  the  ultimate  standard  of  all  our 
weights  and  measures. 

87.  Years  are  divided  into  Civil  and  Solar  years. 

88.  The  Solar  Year  is  equal  to  365  d.  5  hr.  48  min.  49.7  sec, 
or  365J  d.  nearly.*  *In  4  years  this  fraction  amounts  to  about 
1  day.  To  provide  for  this  excess,  1  day  is  added  to  the  mo. 
of  Feb.  every  4th  year,  which  is  called  Leap  Year. 

Note. — Every  year  that  is  exactly  divisible  by  4,  except  centennial 
years,  is  a  leap  year  ;  the  others  are  common  years.     Thus,  1876,  '80,  etc., 
were  leap  years  ;  1879,  '81,  were  common.     Every  centennial  year  exactly 
divisible  by  400  is  a  leap  year ;  the  other  centennial  years  are  common.  . 
Thus,  1600  and  2000  are  leap  years  ;  1700,  1800,  and  1900  are  common. 

89.  The  Civil  Year  includes  both  common  and  leap  years, 
and  is  divided  into  12  Calendar  months,  viz : 


January 

(Jan.) 

31  days. 

July 

(July) 

31  days. 

February 

(Feb.) 

28     " 

August 

(Aug.) 

31      " 

March 

(Mar.) 

31      " 

September 

(Sept.) 

30     " 

April 

(Apr.) 

30     " 

October 

(Oct.) 

31     " 

May 

(May) 

31      " 

November 

(Nov.) 

30     " 

June 

(June) 

30     " 

December 

(Dec.) 

31      " 

Laplace,  Somerville,  Baily's  Tables. 


Miscellaneous  Tables. 


37 


90.  A  Calendar  is  a  division  of  time  into  different  periods, 
adapted  to  the  wants  of  society. 

91.  The  first  Civil  Calendar  worthy  of  notice  was  estab- 
lished by  Julms  Caesar  46  years  before  Christ,  and  continued 
in  use  until  the  adoption  of  the  Gregorian  Calendar  in  1582. 

Dates  prior  to  the  adoption  of  the  Gregorian  Calendar  are  called  old 
style,  and  are  marked  0.  S. ;  those  since  are  called  new  style,  and  are 
marked  N.  S. 

92.  To  change  dates  from  Old  Style  to  New. 

From  1582  to  1700  (1600  being  leap  year)  add  10  days  to 
Old  Style. 

From  1700  to  1800  add  11  days ;   from  1800  to  1900  add 

12  dajss ;   and  from  1900  to  2100  (2000  being  leap  year)  add 

13  days. 

Note. — Russia  continues  to  use  the  Julian  calendar,  or  Old  Style  ; 
hence.,  Russian  dates  are  now  12  days  behind  ours. 


MISCELLANEOUS     TABLES. 


12  things     =     1  dozen. 
12  dozen      =     1  gross. 


12  gross       =     1  great  gross. 
20  things     =     1  score. 

Paper. 


24  sheets 

=     1  quire  of 

paper.      2  reams     =     1  bundle. 

20  quires 

=     1  ream. 

5  bundles  =     1  bale. 

Books. 

2  leaves 

=     1  folio. 

8  leaves     rs     1  octavo,  or  8vo. 

4  leaves 

=     1  quarto, 

or  4to.      12  leaves     =     1  duodecimo,  or  12mo. 

Notes. — 1.  The  terms  folio,  quarto,  octavo,  etc.,  denote  the  number  of 
leaves  into  which  a  sheet  of  paper  is  folded  in  making  books. 

2.  In  copying  legal  papers,  recording  deeds,  etc.,  clerks  are  usually  paid 
by  the  folio.     Thus, 

100  words  make  1  folio  in  New  York. 
72  words      "       1  folio  in  com.  law  in  England. 
90  words      "       1  folio  in  chancery  in  England. 

3.  In  printing  books,  250  impressions  or  125  sheets  printed  on  both 
sides,  make  1  token. 


38  United  States  Money. 

UNITED     STATES    MONEY. 

93.  Money  is  the  measure  of  value. 

94.  Moneys  of  Account  are  those  in  which  accounts  are  kept. 

95.  Currency  is  the  money  employed  in  trade. 

96.  Coins  or  Specie  are  pieces  of  metal  of  known  purity  and 
weight,  stamped  at  the  Mint,  and  authorized  by  Government 
to  be  used  as  money  at  fixed  values. 

97.  Bullion  is  uncoined  gold  or  silver,  and  includes  bars, 
gold-dust,  etc.  c- 

98.  Paper  Money  is  a  substitute  for  metallic  currency.  It 
consists  of  Treasury  Notes  issued  by  the  Government  known 
as  Greenbacks,  and  Bank  Notes  issued  by  banks. 

99.  U.  S.  Money  is  the  legal  currency  of  the  United  States, 
and  is  often  called  Federal  Money.  Its  denominations  are 
Eagles,  Dollars,  Dimes,  Cents,  and  Mills,  which  increase  and 
decrease  by  the  scale  of  ten,  and  it  is  thence  called  Decimal 
Currency. 

Table. 

10  mills  = '  1  cent,    .  .  ct. 

10  cents  =     1  dime,  .  .  d. 

10  dimes,  or  100  cts.  =     1  dollar, .  .  dot.,  or  $. 

10  dollars  =     1  eagle,  .  .  E. 

100.  The  U.  S.  coins  are  gold,  silver,  nickel,  ana  bronze. 

101.  The  Gold  coins  are. the  double  eagle,  eagle,  half  eagle, 
quarter  eagle,  three-dollar  piece,  and  dollar. 

102.  The  Silver  coins  are  the  dollar,  half  dollar,  quarter 
dollar,  and  dime. 

103.  The  Nickel  coins  are  the  5-cent  and  S-cent  pieces. 

104.  The  Bronze  coin  is  the  1-cent  piece. 


United  States  Money.  39 

105.  The  weight  and  purity  of  the  coins  of  the  United 
States  are  regulated  by  the  laws  of  Congress.* 

Notes. — 1.  The  gold  dollar  is  the  Unit  of  Value.  Its  standard  weight 
is  25.8  gr. ;  that  of  the  quarter  eagle,  64.5  gr. ;  of  the  3-dollar  piece,  77.4 
gr. ;  of  the  half  eagle,  129  gr. ;  the  eagle,  258  gr. ;  the  double-eagle,  516  gr. 

2.  When  pure,  gold  is  said  to  be  24  carats  fine.  If  it  contains  18  parts 
of  pure  gold  and  6  parts  of  alloy,  it  is  18  carats  fine,  etc.-  Gold  for 
manufacturing  purposes  varies  from  14  to  18  carats  fine. 

3.  The  weight  of  the  standard  silver  dollar  is  412|  grains  ;  the  half  dol- 
lar, 12|  grams  or  192.9  grains  ;  the  quarter  dollar,  6^  grams,  or  96.45  gr. ; 
the  dime,  2£  grams  or  38.58  grains. 

4.  The  weight  of  the  nickel  5-cent  piece  is  77.16  grains,  or  5  grams; 
of  the  3-cent  nickel,  30  grains;  of  the  cent,  bronze,  48  grains. 

5.  The  standard  purity  of  the  gold  and  silver  coins  is  by  weight  nine- 
tenths  pure  metal,  and  one-tenth  alloy.  The  alloy  of  gold  coins  is  silver 
and  copper;  the  silver,  by  law,  is  not  to  exceed  one-tenth  of  the  whole 
alloy.     The  alloy  of  silver  coins  is  pure  copper. f 

6.  The  5-cent  and  3-cent  pieces  are  composed  of  one-fourth  nickel  and 
three-fourths  copper  ;  the  cent,  of  95  parts  copper  and  5  parts  of  tin  and 
zinc.  They  are  known  as  nickel  and  bronze  coins.  The  diameter  of  the 
nickel  5-cent  piece  is  two  centimeters,  and  its  weight  5  grams. 

7.  The  Trade  Dollar  of  420  grains  is  no  longer  coined. 

106.  Legal  Tender  is  money  which,  if  offered,  legally  satis- 
fies a  debt. 

Notes. — 1.  All  the  gold  coins,  and  the  silver  coins  of  $1  and  upwards, 
except  the  trade  dollar,  are  legal  tender  for  all  payments. 

2.  Silver  coins  less  than  $1  are  legal  tender  to  the  amount  of  $10  ; 
nickel  and  bronze  pieces  to  the  ambunt  of  25  cents. 


CANADA     MONEY. 

107.  Canada  Money  is  the  legal  currency  of  the  Dominion 
of  Canada.  It  is  founded  on  the  Decimal  Notation,  and  its 
denominations,  Dollars,  Gents,  and  Mills,  have  the  same 
nominal  value  as  the  corresponding  denominations  of  U.  S. 
Money.  Hence,  all  the  operations  in  it  are  the  same  as  those 
in  U.  S.  Money. 

*  The  United  States  adopted  the  decimal  system  of  currency  in  1789.  Since  then  it 
has  been  adopted  by  France,  Belgium,  Brazil,  Bolivia,  Canada,  Chili,  Denmark,  Ecuador, 
Greece,  Germany,  Italy,  Japan,  Mexico,  Norway,  Peru,  Portugal,  Spain,  Sweden,  Switz- 
erland, Sandwich  Islands,  Turkey,  U.  S.  of  Colombia,  and  Venezuela. 

t  Report  of  Director  of  the  Mint. 


40  Weights  and  Measures. 


ENGLISH     MONEY. 

108.  English  or  Sterling  Money  is  the  currency  of  Great 
Britain. 

Table. 

4  farthings  (qr.  or  far.)     =     1  penny,     .    .    .    .    d. 
12  pence  =     1  shilling,  ....*. 

20  shillings,  or  i 

10  florins  W    ,  =     1  Pound  or  sovereign,  £.    ^      __ 

21  shillings  =     1  guinea,    .     .    .     .    g. 

109.  The  Unit  of  English  Money  is  the  Pound  Sterling, 
which  is  represented  by  a  gold  Sovereign  equal  in  value  to 
$4.8665.     The  guinea  is  no  longer  coined. 

Notes. — 1.  The  standard  purity  of  the  gold  coins  of  Great  Britain  is 
22  carats  fine ;  that  is,  \^  pure  gold  and  -fa  alloy.  That  of  the  silver  coins 
is  1 1  pure  silver  and  -fa  alloy. 

2.  The  silver  coins  are  the  crown  (5s.) ;  half  crown  (2s.  6d.) ;  florin  (2s.)  ; 
shilling  (12d.) ;  the  six-penny,  four-penny,  and  three-penny  pieces. 

3.  The  copper  coins  are  the  penny,  half-penny,  and  farthing. 

4.  Farthings  are  commonly  expressed  as  fractions  of  a  penny,  as  7|d. 


FRENCH     MONEY. 

110.  French  Money  is  the  national  currency  of  France. 
The  system  is  founded  upon  the  decimal  notation ;  hence,  all 
the  operations  in  it  are  the  same  as  those  in  U.  S.  money.  The 
denominations  are  the  franc,  decime,  and  centime. 

Table. 

10  centimes  (c.)  =     1  decime,  .     .    d. 
10  declines  =     1  franc,      .    .    fr. 

111.  The  Unit  of  French  money  is  the  Franc.  Decimes  are 
tenths  of  a  franc,  and  centimes  are  hundredths. 


French  Money.  41 

Notes. — 1.   Centimes  by  contraction  are  commonly  called  cents. 

2.  Decimes,  like  our  dimes,  are  not  used  in  business  calculations ;  they 
are  expressed  by  tens  of  centimes.  Thus,  5  decimes  are  expressed  by 
50  centimes  ;  63  fr.,  5  d.,  and  4  c.  are  written,  63.54  francs. 

3.  The  legal  value  of  the  franc  in  estimating  duties,  is  19.3  cents;  its 
intrinsic  value  is  a  trifle  more. 

112.  The  Coins  of  France  are  of  gold,  silver,  and  bronze. 

The  Gold  coins  are  the  hundred >  forty,  twenty,  ten,  and/ve 
franc  pieces. 

The  Silver  coins  are  the  five,  tivo,  and  one  franc  pieces,  the 
fifty  and  twenty-five  centime  pieces. 

Bronze  coins  are  the  ten,  five,  two,  and  one  centime  pieces. 

The  gold  and  silver  coins  of  France,  like  those  of  the  U.  S.,  are  ^  pure 
metal  and  ^  alloy. 


GERMAN    MONEY. 

100  pfennigs     =     1  reischmark. 

113.  The  Coins  of  the  New  German  Empire  consist  of  gold, 
silver,  and  nickel. 

The  Gold  coins  are  the  5-mark  piece  called  half  krone  (half 
crown),  the  10-mark  piece  called  krone  (crown),  and  the  20- 
mark  piece  called  doppel  krone  (double  crown). 

The  Silver  coins  are  the  2  and  1  mark  pieces. 

The  Nickel  coins  are  10  and  5  pfennigs  (pennies). 

114.  Reischmark  {Royal  Mark)  is  the  Standard  Unit.  It 
is  equal  to  23.85  cts.  U.  S.  money,  and  is  divided  into  100  equal 
parts,  one  of  which  is  called  a  pfennig. 

Note. — The  coins  most  frequently  referred  to  in  the  United  States  are 
the  Silver  Thaler  which  equals  74.6  cents,  and  the  Silver  Groschen  equal 


eteio    System.* 


[& 


Definitions. 

115.  Metric  Weights  and  Measures  increase  and  decrease 
regularly  by  the  Decimal  Scale. 

116.  The  Meter  is  the  Base  of  the  System,  and  is  one  ten- 
millionth  part  of  the  distance  from  the  Equator  to  the  Pole,  or 
39.37  inches,  nearly. 

Note. — The  term  Meter  is  from  the  Greek  metron,  a  measure. 

117.  The  Metric  System  has  three  principal  units,  the 
Me'ter  (meeter),  Li'ter  (leeter),  and  Gram.  To  these  are 
added  the  Ar  and  Ster,\  for  square  and  cubic  measure.  Each 
of  these  units  has  its  multiples  and  subdivisions. 

118.  The  names  of  the  higher  metric  denominations  are 
formed  by  prefixing  to  the  name  of  the  unit,  the  Greek 
numerals,  Dele' a,  Hek'to,  Kil'o,  and  Myr'ia. 

Thus,  from  Dek'a,     10,       we  have  Dek'ame'ter,  10      meters. 

"      Hek'to,  100,  "        Hek'tome'ter,  100 

"      Kil'o,       1000,         "        Kil'ome'ter,  1000 

*      Myr'ia,  10000,       "        Myr'iame'ter,  10000      " 


*  This  system  had  its  origin  in  France  near  the  close  of  the  last  century.  Its  sim- 
plicity and  comprehensiveness  have  secured  its  adoption  in  nearly  all  the  countries  of 
Europe  and  South  America. 

Rs  use  was  legalized  in  Great  Britain  in  1864,  and  in  the  United  States  in  1866. 

It  Is  adopted  hy  the  TJ.  S.  Coast  Survey,  and  is  extensively  used  in  the  Arts  and 
Sciences,  and  partially  in  the  Mint  and  Post  Office. 

t  The  spelling,  pronunciation,  and  abbreviation  of  metric  terms  in  this  work,  are  the 
same  as  adopted  by  the  American  Metric  Bureau,  Boston,  and  the  Metrological  Soc,  N.Y. 


Metric  System.  43 

119.  The  lower  denominations  are  formed  by  prefixing  to 
the  name  of  the  unit  the  Latin  numerals,  Dec'i,  Certti,  and 
Mil'li. 

Thus,  from  Dec'i,    y1^,      we  have  Dec'ime'ter,    T^     meter. 
"      Cen'ti,  yi^,  *         Cen'time'ter,    T£7 

«      Mil'li,  T^,        "         Mil'lime'ter,    ^      " 

Note. — The  numeral  prefixes  are  the  Key  to  the  whole  system,  and 
should  be  thoroughly  committed  to  memory. 


METRIC     LINEAR    MEASURE. 
Tab  le. 


10  mtt'li-me'ters  {mm.)    —  1  cen'ti-me'ter, 

10  cen'ti-me'ters  =  1  dec'i-me'ter,  . 

10  dec'i-me'ters  =  1  METER,      .     . 

10  me'ters  =  1  dek'a-me'ter, 

10  dek'a-me'ters  —  1  hek'to-me'ter, 

10  hek'to-me'ters  =  1  kil'o-me'ter, 

10  kiVo-me'ters  =  1  myr'ia-me'ter, 


em.  (jU  »»•) 

dm.  (TV  m.) 

m. 

Dm.  (10  m.) 

Hm.  (100  m.) 

Km.  (1000  m.) 

Mm.  (10000  m.) 


Notes. — 1.   The  principal   unit  of  each   table   is  printed  in   capital 
letters ;  those  in  common  use  in  full-faced  Roman. 

2.  The  Accent  of  each  unit  and  prefix  is  on  the  first  syllable,  and 
remains  so  in  the  compound  words. 

3.  Abbreviations  of  the  higher  denominations  begin  with  a  capital, 
those  of  the  lower  begin  with  a  small  letter. 

Common     Equivalents. 

1  cen'timeter  =  0.3937  inches. 

1  dec'imeter  =  3.937        " 

1  me'ter  =  39.37*      " 

1  kil'ometer  =  0.6214  mile. 

4. — Merchants  usually  reckon  the  meter  as  1TV  yard. 
ONE    DECIMETER. 


i  t  1 1 1 T  1 1 1 1 1 1 1 1  f  1 1 1 1 1 1 1 1 1 1 T  1 1 1 1 1 « 1 1 1 1  i  f  I II  i  il  1 1 1 1 1 1  1 1 1 1 1 1 1 1 1 1 1  ii  1 1 1 1 1  Li  1 1 1 1 1 1  f  1 1  ■  1 1  H 1 1  Ti  1 1 1 1 1 1 1 1 1 1 


100  Millimeters. 


*  Established  by  Act  of  Congress  in  1866. 


44  Weights  and  Measures. 

120.  The  Meter  is  the  Standard  Unit  of  length,  and,  like 
the  yard,  is  used  in  measuring  cloths,  laces,  short  distances,  etc. 

121.  The  Kilometer,  like  the  mile,  is  used  in  measuring 

long  distances.  * 

>. 

122.  The  Centimeter  and  Millimeter  are  used  for  minute 
measurements,  as  the  thickness  of  glass,  paper,  etc. 

Note. — The  compound  words  may  be  abbreviated  by  using  only  the 
prefix  and  the  first  syllable  or  letter  of  the  unit ,  thus,  centimeter,  milli- 
meter, centiliter,  milliliter,  centigram,  decigram,  may  be  called  centim, 
millim,  centil,  decig,  etc. 

123.  The  approximate  length  of  1  meter  is  40  in.;  of  1 
decim.,  4  in.;  of  5  meters,  1  rod;  of  1  kilom.,  §  mile. 

Note. — Decimeters,  dekameters,  hektometers,  like  dimes  and  eagles,  are 
seldom  used. 

124.  Since  meters,  centimeters,  and  millimeters,  correspond 
to  dollars,  cents,  and  mills,  it  follows  that  metric  numbers  may 
be  read  like  U.  S.  Money.  Thus,  28.375  meters  are  read  28 
and  375  thousandths  meters,  or  28  m.  3  dm.  7  cm.  5  mm.,  or 
28  m.  37  cm.  5  mm. 

1.  Read  in  meters  15 'Dm.;  78  Hm.;  355  Km.;  49.237  dm.; 
3.54  Mm. 

125.  To  write  Metric  Numbers  decimally  in  terms  of  a  given  Unit. 

2.  Write  9  Hm.  4  m.  6  dm.  8  cm.  in  terms  of  a  meter. 

Explanation. — We  write  meters  in  units  place,  operation. 

on  the  left  of  the  decimal  point,  the  Dm.  in  tens      904.68  m.,   Ans. 
place,    the  Hm.   in  hundreds  place,  etc.,  and  the 

decims.  in  tenths  place,  centims.  in  hundredths,  etc.,  as  we  write  the  orders 
of  integers  and  decimals  in  simple  numbers.     Hence,  the 

Kule. —  Write  the  given  unit  and  the  higher  denomi- 
nations in  their  order,  on  the  left  of  a  decimal  point,  as 
integers,  and  those  below  the  unit,  on  the  right,  as 
decimals. 

Note. — If  any  intervening  denominations  are  omitted  in  the  given 
number,  their  places  must  be  supplied  by  ciphers. 


Metric  System,  45 

3.  Write  in  terms  of  a  meter  15  Dm.  Ans.  150  m. 

4.  Write  in  meters  254  Dm.  42  cm. 

5.  Write  385  Hm.  24  mm. 

6.  Write  172  Hm.  32  Dm.  in  meters. 

7.  Write  8  Km.  9  Hm.  6  Dm.  8  mm. 

8.  Write  in  meters  and  decimals  4  Mm.  15f  Dm.  7  cm. 
5  mm. 

9.  Write  in  Km.  37  Mm.  64  Dm.  37£  m.  8  dm.  7  mm. 

126.  To  reduce  Metric  Numbers  from  higher  denominations  to 
lower,  and  from  lower  to  higher. 

10.  Reduce  352  meters  to  millimeters. 

OPERATION. 

Solution.  —  Since    1    m.  =  1000    mm.,    352  ^52  m. 

meters  =  352  x  1000,  or  352000  mm.,  Ana.  1000 

Ans.  352000  mm. 
n.  Change  843000  millimeters  to  meters. 

Solution. — Since  1000  mm.  =  im.  843000  mm.  =  as  many  meters  as 
1000  is  contained  times  in  843000.  Pointing  off  three  decimal  places 
divides  a  number  by  1000.     Ans.  843.000  m.     Hence,  the 

Rule. — Move  the  decimal  -point  one  place  to  the  right 
or  left,  as  the  case  may  require,  for  each  denomination 
to  which  the  given  number  is  to  be  reduced. 

12.  Change  75.25  Km.  to  meters.  Ans.  75250  m. 

13.  Change  8427.83  meters  to  Hm.         Am.  84.2783  Hm. 

14.  Change  9723.8  m.  to  Km.  Ans.  9.7238  Km. 

15.  Change  83605.24  cm.  to  meters  and  decimals.     To  Dm. 

16.  Change  75842  mm.  to  meters  and  decimals.    To  cm. 

17.  Reduce  187.62  dm.  to  meters.     To  cm. 

18.  Reduce  61.75  Km.  to  cm.     To  mm. 

19.  Reduce  158364  mm.  to  Hm. 

20.  Reduce  28.53  Km.  to  dm. 

21.  Reduce  153  Mm.  to  Dm.     To  cm. 


46 


Weights  and  Measures. 


METRIC     SQUARE    MEASURE. 

127.  The  Measuring  Unit  of  Surfaces  is  a  Square,  each  side 
of  which  is  a  Linear  Unit. 

Table. 


100  sq. 

milli-me'ters  (sq.  mm 

)  =     1  sq.  cen'ti-me'ter, 

sq.  em. 

100  sq. 

cen'ti-me'ters 

=     1  sq.  dec'i-me'ter, 

sq.  dm. 

100  sq. 

dec'i-me'ters 

_  jl  SQ.  METER,       . 

(     or  cent/ar,    .     . 

sq.  m. 
ca. 

100  sq. 

me'ters 

j  1  sq.  dek'a-me'ter, 
(     or  Ar,      .     .     . 

sq.  Dm. 
A. 

_  ( 1  sq.  hek'to-me'ter, 
(     or  hek'tar,  .     . 

sq.  Hm. 

100  sq. 

dek'a-me'ters 

Ha. 

100  sq. 

hek'to-me'ters 

=     1  sq.  kil'o-me'ter, 

sq.  Km. 

Common 

EQU  1  VALE  NTS. 

1  sq.  centim. 

=a        0.1550  sq.  in. 

1  sq.  decim. 

=         0.1076  sq.  ft. 

1  sq.  meter 

=         1.196  sq.  yd. 

1  ar 

=        3.954  sq.  rods. 

1  hektar 

=        2.471  acres. 

1  sq.  kilo 

=        0.3861  sq.  mile. 

128.  The  sq.  meter  is  used-  in  measuring  ordinary  surfaces, 
as  floors,  ceilings,  etc. ;  the  ar  and  hektar  in  measuring  land ; 
and  the  sq.  kilometer  in  measuring  States  and  Territories. 

Note. — The  term  ar  is  from  the  Latin  area,  a  surface. 

129.  The  approximate  area  of  a  sq.  meter  is  lOf  sq.  ft.,  or 
H  S(l-  jd- >  ai*d-  °^  ^ne  hektar  about  2  J  acres. 


130.  The  scale  of  surface  measure  is  100  (10  x  10). 
That  is,  100  units  of  a  lower  denomination  make  a 
unit  of  the  next  higher ;  hence,  each  denomination 
must  have  two  places  of  figures. 


Sq.  Centim. 


Thus,  23  Ha.  19  A.  25  ca.,  written  as  ars,  is  2319.25  A.,  and  may  he  read 
"2319  ars  and  25  centars"  If  written  as  hektars,  it  is  23.1925  Ha.,  and 
may  he  read  "23  hektars  and  1925  centars," 


Metric  System.  47 

22.  Express  86.34  A.  as  centars.     As  Hektars. 

23.  Write  75  sq.  m.  as  sq.  mm.     As  sq.  dm. 

24.  In  8234  ca.  how  many  A.? 

25.  In  184.38  A.  how  many  Ha.  ? 

METRIC     CUBIC     MEASURE. 

131.  The  Measuring  Unit  of  solids  is  a  Cube,  the  edge  of 
which  is  a  Linear  Unit. 

Table. 

1000  cu.  mil'li-me'ters  {cu.  mm.)  =  1  cu.  cen'ti-me'ter,  cu.  cm. 

1000  cu.  cen'ti-me'ters  =  1  cu.  dec'i-me'ter,  cu.  dm. 

1000  cu.  dec'i-me'ters  =  1  CU.  METER,  .     .  cu.  m. 

10  dec'i-sters  =  1  STER,  .     .     .     .  st. 

10  sters  =  1  dek'a-ster,    .     .  Dst. 

Common     Equivalents. 

1  cu.  centimeter        =        0.061  cu.  in. 
1  cu.  decimeter  =        61.022  cu.  in. 

1  cu.  meter  =        1.308  cu.  yds. 

Note.— The  ster  =  .2759  cord  is  seldom  used. 

132.  The  cubic  meter  is  used  in  measuring  ordinary  solids, 
as  timber,  excavations,  embankments,  etc. 

When  applied  to  fire-wood,  it  is  sometimes  called  a  Ster,  and 
is  equal  to  about  35J  cubic  feet. 

Note. — The  cubic  decimeter,  when  used  as  a  unit  of  dry  or  liquid 
measure,  is  called  a  Liter, 

133.  The  scale  of  cubic  measure  is  1000  (10  x  10 
x  10) ;  hence,  each  denomination  must  have  three 
places  of  figures. 

Cu.  Cm. 

26.  Express  18000  cu.  mm.  as  en.  cm.  Ans.  18.000  cu.  cm. 

27.  Write  28  cu.  m.  and  15  cu.  dm.  as  cu.  meters. 

Ans.  28.015  cu.  m. 

28.  Write  in  centimeters  256  cu.  dm,  34  cu,  cm.  89  cu,  mm. 


48 


Weights  and  Measures. 


29.  In  38450  cu.  dm.  how  many  meters  ? 

30.  In  253  cu.  m.  how  many  cu.  mm.?    Cu.-em.? 


METRIC     DRY    AND     LIQUID     MEASURE. 

134.  The  Liter  is  the  principal  unit  of  Dry  and  Liquid 
Measure,  and  is  equal  in  volume  to  a  cubic  decimeter. 

Table. 


10  mirii-li'ters  (ml.) 

=     1  cen'ti-li'ter,    . 

.    .    cl. 

(ikO 

10  cen'ti-li'ters 

=     1  dec'i-li'ter,  .    . 

.    .    dl. 

(tV  *0 

10  dec'i-li'ters 

=      1   LITER,     .     .     . 

.    .    1. 

10  li'ters 

sb     1  dek'a-li'ter,     . 

.    .    Dl 

(101) 

10  dek'a-li'ter 

=     1  hek'to-li'ter,    . 

.    .    El. 

(100  I.) 

10  hek'to-li'ters 

=     1  kil'o-li'ter,  .     . 

.     .    Kl. 

(1000  I) 

10  kil'o-li'ters 

ss     1  myr'ia-li'ter,    . 

.     .    Ml. 

(10000  I.) 

1  cubic  centimeter  =  1  milliliter  of  water. 


Common     E 

QUI VA LENTS. 

1  liter               bb 

61.022  cu.  inches. 

1  liter               = 

1.0567  liquid  quarts 

1  liter               = 

0.908  dry  quarts. 

1  hektoliter      = 

3.531  cu.  feet. 

1  hektoliter      = 

26.417  gallons. 

1  hektoliter      ss 

2.837  bushels. 

Notes. — 1.  The  Centiliter  is  a  little  less  than  |  gill,  and  is  used  for 
measuring  liquids  in  small  quantities. 

2.  The  Liter  is  used  in  measuring  milk,  wine,  and  small  fruits,  and  is 
about  equal  to  a  quart. 

3.  The  Hektoliter  is  used  in  measuring  grain  and  liquids  in  casks,  and 
is  equal  to  about  26|  gal.,  or  2f  bushels. 

•  31.  In  128.653  ml.  how  many  dl.?    How  many  cl.? 

32.  Write  35  1.  as  cl.     As  ml.    As  Dl. 

33.  How  many  liters  in  a  cistern  measuring  2  cu.  meters  ? 

34.  How  many  Dekaliters  in  such  a  cistern  ?  How  many  HI.? 


Metric  System. 


49 


METRIC     WEIGHT. 

135.  The  Gram  is  the  principal  unit  of  weight,  and  is  equal 
to  a  cubic  centimeter  of  distilled  water  at  its  greatest  density, 
viz.,  at  4°  Centigrade,  or  39.2°  Fahrenheit. 


10  milli-grams  (rng.)  = 

10  cen'ti-grams  = 

10  dec'i-granis  = 

10  grams  == 

10  dek'a-grams  = 

10  hek'to-grams  = 

10  kil'o  grams  = 


Table. 

1  cen'ti-gram, 
1  dec'i-gram, . 
1  GRAM,  .  . 
1  dek'a-gram 
1  hek'to-gram, 
1  kil'o-gram, 


dg. 

9- 

Dg. 
Hg. 
Kg. 


(tV  <h) 

(10  g.) 
(100  g.) 
(1000  g.) 


1  myrla-gram,   .     Mg.      (10000  </.) 


100  myr'ia-grams  =     1  tonneau  or  Ton,  T. 


i 


lDg. 


Idg. 


ldg. 


leg. 


© 

lmg. 


Common     Equivalents. 


1  gram 
1  kilogram 
1  metric  ton 


gram 
gram 
kilogram 
metric  ton 


=  11 


cu.  centim.,  or 
millil.  of  water, 
cu.  decim.,  or 
liter  of  water, 
cu.  meter,  or 
kiloliter  of  water. 

=     15.432  grs.  Troy. 

=     0.03527  oz.  Av. 

=     2.2046  lbs.  Av. 

=     1.1023  tons. 


50  Weights  and  Measures. 

136.  The  Gram  is  used  in  weighing  gold,  silver,  jewels,  and 
letters,  and  in  mixing  medicines. 

137.  The  Kilogram  (often  called  kilo)  =  %\  lb.  nearly,  is 
used  in  weighing  common  articles ;  as  sugar,  tea,  butter,  etc. 

Note. — The  Quintal  =  10  Mg.,  or  100  Kilos,  is  seldom  used. 

The  Metric  ton  of  about  2200  lb.  is  used  in  weighing  heavy 
articles ;  as  hay,  coal,  etc. 

Note. — The  nickel  5 -cent  piece  weighs  1  gram.  The  weight  of  a  letter 
for  single  postage  must  not  exceed  15  grams,  or  3  nickels. 

35.  Write  23.847  g.  as  dg.;  as  eg.;  as  Dg.;  as  mg. 

36.  In  2.5384  mg.  how  many  dg.?     How  many  grams  ? 

37.  In  2.158  Kg.  how  many  grams  ?     How  many  eg.? 

38.  What  decimal  of  a  Kg.  will  be  equal  to  1  gram  ? 

39.  Express  in  grams,  31.0006  Tons. 

138.  Metric  weights  and  measures  are  added,  subtracted, 
multiplied,  and  divided  in  the  same  manner  as  decimals  or 
U.  8.  Money,  and  therefore  require  no  special  rules.  (Complete 
Graded  Arith.,  Arts.  252-261.) 

139.  To  Reduce  Metric  to  Common  Weights  and  Measures. 

1.  In  387  cm.  how  many  feet  ? 

Explanation.  —  Since  1  meter  (the  1  meter  r=  39.37  in. 

principal  metric  unit)  is  equal  to  39.37  337  cm<  _     3,87  m. 
in.,  3.87  meters  are  equal  to  39.37  x  3.87,  — —  . 

or  152.3619  inches.      These  reduced  to  **  )  15^.3619  inches, 

feet  are  12.69+  ft.     Hence,  the  A)IS.    12. 6968 J  ft. 

Kule. — Multiply  the  value  of  the  principal  metric  unit 
of  the  Table  by  the  given  metric  number  expressed  in  the 
same  unit,  and  reduce  the  product  to  the  denomination 
required,     (Art.  148.) 

2.  Describe  the  standard  unit  of  weight  m  the  Metric 
System. 

3.  How  many  pounds  in  84  kilograms  f    4ws.  185,1864  lbs. 


Metric  System.  51 

4.  Change  25  HI.  into  bushels. 

5.  Express  85  liters  in  gals. 

6.  Reduce  360  Km.  to  miles. 

7.  Change  864  eg.  to  ounces. 

8.  In  84  ars  how  many  sq.  rods  ? 

Solution. — One  ar.  =  3.954  sq.  r. ;  hence,  84  ars  s  3.954  x  84,  or 
332.136  square  rods,  Am. 

9.  In  80. 75  Ha.  how  many  acres  ? 
10.  Change  250  cu.  m.  to  cu.  feet. 

140.   To  reduce  Common  to  Metric  Weights  and  Measures. 

11.  How  many  Km.  in  3758  yds.  2  ft.  6  in.? 

Explanation. -The  given  com-  3758  ?d'  2  ft*  6  in' 

pound    number    reduced     to    inches  £ 

=  135318  in.     Dividing  this  number  11276 

by  39.37,  the  number  of  inches  in  a  in 

meter,  reduces  the  given  number  to  

meters.     Removing  the  decimal  point      o9.o7  )  lo5ol8  inches. 

3  places  to  the  left  gives  the  number  3437.084+  m. 

of  kilometers.     Hence,  the  .         0,0WA0,   ,    -^ 

Ans.  3.437084+  Km. 

Rule. — Divide  the  given  number  by  the  value  of  the 
principal  metric  unit  of  the  Table,  and  reduce  the  quo- 
tient to  the  denomination  required. 

Note. — Before  dividing,  the  given  number  should  be  reduced  to  the 
denomination  in  which  the  value  of  the  principal  metric  unit  is  expressed. 

12.  Reduce  2J  yd.  to  cm. 

13.  Change  24  lbs.  3  oz.  to  grams. 

14.  Reduce  28  qts.  1  pt.  to  centiliters. 

15.  In  84.326  acres  how  many  ars  ? 

16.  Express  an  acre  as  the  decimal  of  a  hectar.     (Art.  130 ) 

17.  In  a  farm  containing  150  A.  19  sq.  r.  how  many 
hectars  ? 

18.  How  many  lb.  Av.  in  a  quintal,  if  1  Dg.  =:  .3527  oz.? 

19.  How  many  5-Qent  pieces  may  be  coined  from  3  lb,  §  ogt 
Of  meta]  ? 


52  Weights  and  Measures. 


Examples. 

1.  Express  the  sum  of  325.6  dm.,  2064.3  cm.,  17.654  m., 
23.8  Dm.,  and  2.583  Km.,  in  terms  of  a  meter. 

32.56 
Explanation. — The  numbers  are  first  reduced  20.643 

to  meters,   the  principal    unit  of    the  table,    by  17  P^A 

removing  the  decimal  point  to  the  right  or  left  as 
in  the  margin  ;   they  are  then  added  as  in  deci- 


238.000 


mals.  ^583.000 

Am.  2891.857  m. 

2.  Add  238  cm.,  438.4  dm.,  52  m.,  82  Hm,  and  2.5  Km. 

3.  What  is  the  difference  between  128.6  dl.  and  34.5  HI.  ? 

Solution.—  3450  liters- 12. 86  liters  =  3437.14  liters,  Am. 

4.  By  how  much  is  35  m.  7  cm.  less  than  the  average  of 
34  m.  2  dm.,  37  m.  8  dm.,  36  m.  9  dm.,  35  m.  7  dm.,  36  m. 
6  dm.,  and  34  m.  8  dm.  ? 

5.  The  circumference  of  a  circular  court  is  48  m.  4  dm. ; 
how  many  Km.  should  I  walk  by  going  8  times  around  it  ? 

6.  A  service  of  plate  weighed  respectively  4  Kg.  9  Dg., 
15  Hg.  5  dg.,  1  Kg.  560  g.,  and  35947  eg. ;  what  is  its  value  at 
%\\  an  ounce  ? 

7.  How  much  does  its  weight  fall  short  of  8J  Kg.  ? 

8.  From  Paris  to  Madrid  is  1450  Km. ;  how  many  miles  per 
hour  does  a  train  go  which  makes  the  trip  in  36  hours  ? 

9.  What  cost  a  pile  of  wood  42.5  m.  long,  2  m.  wide,  and 
1.9  m.  high,  at  $2  per  ster  ? 

10.  If  35  Kg.  of  beef  cost  50  fr.  40  c,  what  is  the  cost  of 
1  Kg.  ?    Of  23£  Kg.  ?     Of  9  Kg.  5  dg.  in  IT.  S.  Money  ? 

n.  A  merchant  buys  2f  Hm.  of  silk  for  $480,  and  sells  it  at 
$1.95  a  yard  ;  how  much  does  he  gain  or  lose  ? 

12.  Bought  454  bu.  of  wheat  at  $3  a  bu.,  and  sold  it  for 
$8.75  a  HI. ;  what  is  the  gain  ? 

13.  In  a  public  office,  35  fires  consume  336  sters  of  wood ; 
what  is  the  average  consumed  by  each,  and  what  its  cost  at 
75  centimes  a  ster? 


Foreign  Weights  and  Measures.  53 


FOREIGN    WEIGHTS    AND    MEASURES. 

141.  The  Metric  System  is  in  general  use  in  the  following 
countries : 

Argentine  Confederacy,  Austria,  Belgium,  Chili,  Colombia, 
Ecuador,  Egypt,  France,  Germany,  Greece,  Italy,  Japan, 
Mexico,  Netherlands,  Peru,  Spain,  Switzerland,  Turkey,  Uru- 
guay, and  Venezuela. 

142.  The  Metric  System  is  permissive,  and  in  partial  use : 

In  Great  Britain,  United  States,  India,  Norway,  Sweden, 
Denmark,  and  Kussia. 

143.  In  Bolivia,  though  the  Metric  is  the  legal  system,  the 
old  Spanish  weights  and  measures  are  used  to  some  extent. 

In  Brazil  the  freight  of  ships  is  estimated  by  the  English  ton 
of  2240  lbs. 

Canada,  Cape  of  Good  Hope,  Liberia,  and  Ceylon  use  the 
same  as  Great  Britain.  The  following  are  often  met  in 
Market  reports : 

144.    In    China  and    Hong    Kong. 

1  tael  =        1£     oz.  Av. 

1  catty  =        li     lb.   " 

1  picul  =    133i     lb.  " 

1  chili  =       14.1    in. 

1  chang  =      11.75  ft. 

In  Denmark. 

1  pound  =  1.102  lb.  Av. 

1  centner  =  110.23    lb.     " 

1  tonde,  grain  =  3.948  U.  S.  bu. 

1      "      coal  =  4.825      "       " 

1  fod(foot)  =  1.03        "      ft. 

1  viertel  =  2.04        *      gal. 

1  alen  (Ell)  =  .684      "     yds. 

Note. — In  coinage  the  metric  system  is  used. 


54  Weights  and  Measures. 

145.  In  Siam,  1  tael  =  1-J  oz.  Av.    The  Picul,  Catty,  and 
Chang,  are  like  Java. 

In    Java. 

1  Ams.  pond     =        1.09  lb.  Av.  1  catty      =    1*  lb.  Av. 

1  picul  =    133£     lb.    "  1  chang    =    4    yd. 

In    Russia. 

1  pound  =  ^    lb.  Av. 

1  pood  (63  to  a  ton)     =  36        lb.    " 

1  berkowitz  =  360        lb.    " 

1  chetvert  —  5.956  U.  S.  bu. 

1  vedro  =  3.25       "    gal. 

1  arsheen  =  28        in. 

1  ship  last  =  2        tons. 

In     India. 

1  Bombay  maund  of  40  seers     =    28     lb.  Av. 


1                        "42    " 

= 

29.4  lb.    M 

1  Bombay  candy  of  20  maunds 

560     lb.    « 

1  Surat  maund  of  40  seers 

= 

3U   ib.    - 

1                    "42    " 

r= 

39^    lb.    " 

!                    "44    " 

= 

41TVlb.    - 

1  Bengal  factory  maund 

r= 

74|   lb.    " 

1  Bengal  bazaar  maund 

— 

82|    lb.  Av. 

1  Madras  maund 

= 

25      lb.    " 

1        "       candy  (20  maunds) 

= 

500      lb.    " 

1  Travancore  "            " 

= 

660      lb.    - 

1  tola 

= 

180      gr. 

1  guz,  Bengal 

= 

1      yd.  Eng. 

1  Corge  pound 

= 

2      lbs.  Av. 

146."  In  Spain  and  many  South  American   States  and  in 
Cuba: 

1  libra  =      1.0141b.  Av.  1  quintal  (100  lib.)  =  101.44   lb.  Av. 

1  arroba  =     25.36    lb.    "  1  vara                      =        .914  yd. 


IK* 

m  EDUCTION 


147.  Reduction  is  changing  Compound  Numbers  from  one 
denomination  to  another  without  altering  their  vaZt/e.  It  is 
of  two  kinds,  Descending  and  Ascending. 

148.  Reduction  Descending  is  changing  higher  denomina- 
tions to  loiver  ;  as,  yards  to  feet,  etc. 

149.  To  reduce  Higher  denominations  to  Lower, 

1.  Eeduce  23  bbl.  4  gal.  3  qt.  to  quarts. 

Explanation.— Since  31|  gal.  make  1  bbl.  23    bbl.  4  gal.  3  qt. 

there    are    3H    times    as    many  gallons  as  31 J 

barrels,  and  7241+4  =  728|  gallons.     Like-  "toqjl       l 
wise,  there  are  4  times  as  many  quarts  as  gal-  2  ° 

Ions,  and  (728J  x  4)  +  3  =  2917  quarts.    Hence,  Z 

the  2917    qt.,  A?is. 

Rule.  —  Multiply  the  highest  denomination  by  the 
number  required  of  the  next  lower  to  make  a  unit  of  the 
higher,  and  to  the  product  add  the  loiver  denomination. 

Proceed  in  this  manner  with  the  successive  denomina- 
tions, till  the  one  required  is  reached. 

2.  In  17  days,  18  hours,  27  minutes,  how  many  seconds  ? 

3.  How  many  sec.  in  the  circumference  of  a  circle? 

4.  Change  12  mi.  8  rd.  3  yd.  2  ft.  to  inches. 

5.  Reduce  83  cu.  yd.  to  en.  in. 

6.  Reduce  243  lb.  3  oz.  6  pwt.  to  grains. 

7.  Reduce  16  T.  8  cwt.  29  lb.  to  pounds. 

8.  Reduce  18  A.  22  sq.  r.  25  sq.  yd.  to  sq.  ft. 

9.  How  many  feet  and  inches  would  a  man  go  in  walking 
2J  miles  ? 


56  Compound  Numbers. 

10.  What  cost  250  miles  of  telegraph  wire,  at  3  cents  a  foot  ? 

11.  What  cost  253  lb.  6  oz.  of  silver,  at  6 J  cts.  a  penny- 
weight ? 

12.  A  school  feast  for  73  children  cost  £3  2s.  4Jd.;  how  many 
farthings  each  did  it  cost  ? 

13.  What  cost  27  T.  3  cwt.  15  lb.  of  potash,  at  $3.87£  per 
cwt.  ? 

150.  Reduction  Ascending  is  changing  lower  denominations 
to  higher  ;  as,  feet  to  yards,  etc. 

151.  To  reduce  Lower  denominations  to  Higher. 

14.  Eednce  67031  far.  to  pounds,  shillings,  and  pence. 

Explanation.  —  Since  4  far.  =  Id.,  67031  4  )  67Q31  far- 

far.  =  as  many  pence  as  4  is  contained  times  12  )  16757d.  3  far. 

in  67031  far.,  or  16757d.  and  3  far.  over.     So,  20^  139Ps  51 

dividing  the  pence  by   12    reduces    them    to  I 

shillings,  and  dividing    the    shillings    by    20  £69  16s. 

reduces  them  to  pounds.    Hence,  the  Ans.   £69  16s.  52 d. 

Eule. — Divide  the  given  denomination  by  the  number 
required  to  make  one  of  the  next  higher. 

Proceed  in  this  manner  with  the  successive  denomina- 
tions, till  the  one  requireol  is  reached.  The  last  quotient, 
with  the  several  remainders,  will  be  the  answer. 

Note. — The  remainders  are  the  same  denomination  as  the  respective 
dividends  from  which  they  arise. 

15.  Reduce  2690  inches  to  rods,  yards,  etc. 

Ans.  13  r.  2£  yd.  2  ft.  2  in.,  or  13  r.  3  yd.  8  in. 

16.  Reduce  642518  gr.  to  pounds. 

17.  Reduce  24748  pt.  to  bushels. 

18.  Reduce  384634  sec.  to  days. 

19.  Reduce  748490  cu.  ft.  to  cords. 

20.  Reduce  864138  gi.  to  barrels. 

21.  Reduce  3187463  sq.  yd.  to  acres. 

22.  Reduce  2835468  sheets  to  reams. 


Reduction.  57 

23.  Eeduce  160750  links  to  miles. 

24.  What  cost  12760  lb.  of  hay,  at  $9.50  per  ton  ? 

25.  What  will  350  rd.  of  stone  wall  cost,  at  31  cents  a  foot? 

26.  How  many  acres  in  350  city  lots,  each  25  by  100  ft. 

27.  A  jewel  weighing  2  oz.  16  pwt.  14  gr.  was  sold  for  $1.38 
per  grain  ;  what  was  the  amount  paid  for  it  ? 


DENOMINATE    FRACTIONS. 

152.  Denominate  Fractions  are  fractions  of  denominate 
Integers,  and  may  be  common  or  decimal. 

153.  To  reduce  Denominate  Fractions,  Common  or  Decimal,  of 
higher  denominations,  to  Integers  of  lower  denominations. 

28.  Reduce  -fa  A.  to  lower  denominations. 

BY  COM.  PKACTIONS.  BY  DECIMALS. 

_^Xl60    =    1440  15  A  =  -36   acres. 

25  25   '  °r      25  sq"r'  160  sq.r.  mi  a. 

15  x   30}=  453J         1Q3|  57.60  sq.r. 

25  25  25  oOf  sq.  yd.  in  1  r. 

3f  x     9  =  j53£  8|  18.15  sq.yd. 

25  25,0r         25Sq'ft  9    sq.ft.  in  1  sq.yd. 

8}xl44  =   1260    KA2  1.35  sq.ft. 

25        "25" '  °r  5°5  "* *      _144  sq.  m.  m  1  sq. ft. 

Ans.  57  sq.r.  18  sq.yd.  1  sq.ft.  50f  sq.in.  50.40  sq.  in. 

Ans.   57  sq.  r.  18  sq.  yd.  1  sq.  ft.  50.4  sq.  in. 

Note. — Only  the  fractional  or  decimal  parts  are  multiplied.  Pointing 
off  2  decimals  in  the  several  products  is  equivalent  to  dividing  them  by 
100,  the  denominator  of  the  given  decimal.     Hence,  the 

Eule. — Multiply  the  given  fraction  or  decimal  by  the 
successive  numbers  which  will  reduce  a  unit  of  the  given 
fraction  to  the  denomination  required,  and  divide  each 
■product  by  the  given  denominator. 

Or,  Cancel,  multiply,  and  reduce  the  result. 


58  Compound  Numbers. 

29.  Reduce  -J  bu.  to  integers  of  lower  denominations. 

SOLUTION. 

J  X  f  x  f  =  28  qt.,  or  3  pk.  4  qt.,  Ans. 

30.  Reduce  |-  mi.  to  integers. 

31.  Reduce  -f  bu.  to  pecks,  etc. 

32.  Reduce  ^-f-g-  gal.  to  lower  denominations. 

33.  Reduce  .458  cwt.  to  lb.,  etc. 

34.  Reduce  .8975  wk.  to  days,  etc. 

35.  Reduce  -§-  lb.  Troy  to  pwt. 

36.  Reduce  .815625  lb.  to  Troy  oz.,  etc. 

37.  Reduce  .3945  day  to  hr.,  etc. 

38.  Reduce  .845  mi.  to  fur.,  rods,  etc. 

39.  How  many  sq.  ft.  in  a  lot  lof  r.  long  and  12f  r.  wide  ? 

40.  How  many  cu.  J-  in.  are  contained  in  1  cu.  inch  ? 

154.   To    reduce   Denominate   Integers  or  Fractions  of  lower,  to 
Fractions  (either  Common  or  Decimal)  of  higher  denominations. 

41.  Reduce  4s.  5d.  to  the  common  fraction  of  a  pound. 
Solution.— 4s.  5d.  =  53d.  £1  =  240d.  Ans.  ££fc. 

42.  Change  7  fur.  29  r.  to  the  fraction  of  a  mile. 


7  fur.  29  r.      =  309  r. 

40)29.00          rods. 

1  mile              =  320  r. 

8)7.725          far. 

Ans.  Mini.   =  .965625. 

Ans.  .965625  m. 

Rule. — Reduce  the  given  compound  number  to  the 
lowest  denomination  mentioned  for  the  numerator,  and 
a  unit  of  the  required  fraction  to  the  same  denomina- 
tion  for  the  denominator. 

For  decimals,  divide  the  given  numbers  as  in  reducing 
integers  to  higher  denominations.     (Art.  151. ) 

Note. — If  the  lowest  denomination  of  the  given  number  contains  a 
fraction,  the  number  must  be  reduced  to  the  parts  indicated  by  the 
denominator  of  the  fraction. 


Addition.  59 

43.  Reduce  f  pwt.  to  the  fraction  of  a  pound  Troy.     (Com- 
plete Graded  Arith.,  Art.  179,  2°.) 

SOLUTION. 

3  3  1    ,,       , 

=  -7-j—  lb.,  Ans. 


8x20x12        8x20x*2        640 

4 

44.  Reduce  8  oz.  5  pwt.  3  gr.  to  the  decimal  of  a  pound. 

45.  Reduce  14s.  8d.  to  the  decimal  of  £1. 

46.  Reduce  0.87259  yd.  to  the  decimal  of  1  m. 

47.  Reduce  \%  pwt.  to  the  fraction  of  1  lb.  Troy. 

48.  Reduce  .45  pt.  to  the  decimal  of  1  gal. 

49.  Reduce  9f  hr.  to  fraction  of  1  week. 

50.  Reduce  -^  cwt.  to  fraction  of  1  ton. 

51.  What  cost  2  bales  3  bun.  1  rm.  4  qr.  21  sheets  of  paper, 
at  $46.87|  a  bundle  ? 

52.  How  much  will  it  cost  to  dig  a  cellar  40  ft.  long,  32  ft. 
wide,  and  5  ft.  deep  ;  at  $0.25  a  cu.  yard. 

155.  To  find  what  part  one  Compound  Number  is  of  another. 

Reduce  the  numbers  to  the  same  denomination,  and  make  the 
number  denoting  the  part  the  numerator,  and  that  tvith  which 
it  is  compared  the  denominator.    (0.  G.  Arith.,  Arts.  226,  249.) 

53.  What  decimal  of  4s.  is  3  pence  ? 

54.  Of  3  gal.  3  qt.  1  pt.  is  1-J  gal.  ? 

55.  Of  1  wk.  3  da.  is  4  da.  4J  hr.? 

56.  Of  16  m.  is  6  miles  30  rods? 

57.  What  decimal  part  of  20  bu.  is  2  pk.  3  qt.  1.2  pt.  ? 

58.  What  decimal  part  of  a  fathom  is  3f  feet? 

ADDITION. 

156.  Compound  Numbers  are  added,  subtracted,  multiplied, 
and  divided  in  the  same  manner  essentially  as  simple  numbers, 
and  require  no  special  rules. 

Note. — 1.  The  apparent  difference  arises  from  their  different  scales  of 
increase,  one  being  variable,  the  other  decimal. 


lb. 

oz. 

pwt. 

gr. 

12 

1 

19 

8 

6 

10 

3 

18 

19 

8 

14 

6 

60  Compound  Numbers. 

1.  Add  12  lb.  1  oz.  19  pwt.  8  gr.,  6  lb.  10  oz.  3  pwt.  18  gr., 
19  lb.  8  oz.  14  pwt.  6  gr. 

Note. — 2.  The  sum  of  the  first  column 
is  32  gr.  =  1  pwt.  8  gr.  Adding  the  1  pwt. 
to  the  next  column,  its  sum  is  37  pwt. 
=  1  oz.  17  pwt.  The  next  column  is  20  oz. 
=  1  lb.  8  oz.  Setting  like  denominations 
in  the  same  column,  the  sum  is  38  lb.  8  oz.  38  8  17  8,  Ans. 
17  pwt.  8  gr. 

2.  Add  78  A.  84  sq.  rd.,  64  A.  32  sq.  rd.,  and  98  A.  45  sq.  rd. 

3.  Add  96  bu.  3  pk.  2  qt.  1  pt.,  46  bu.  3  pk.  1  qt.  1  pi,  2  pk. 
1  qt.  1  pt.,  and  23  bu.  3  pk.  4  qt.  1  pt. 

4.  Add  2  mi.  3  fur.  8  rd.  2  ft,  4  mi.  7  fur.  6  rd.  4  ft.,  12  mi. 
5  fur.  17  rd.  11  ft.,  and  18  mi.  6  fur.  7  rd.  2  ft. 

5.  Add  together  -^fas  hhd.  and  f  gill. 

Note.— 3.  Denominate  Fractions  should  *iiW  nn(*'  =  foil  S]- 

be  reduced  to  integers  and  fractions  of  lower  f  o  32>  or  Y  S1,  —  IT  81, 

denominations,  and  to  a  common  denomina-  -|  gi.  =  T4^  gi. 

tor,  then  added.  Am    ^  gi> 

6.  Find  the  sum  of  £J  f  s.  Jd.  in  integers. 

7.  Add  f  lb.  |-  oz.  f  pwt.  9.  Add  f  wk.  {  d.  If  hr. 

8.  Add  J  gal.  f  qt.  2£  pt.         10.  Add  £|  |s.  4|d. 


SUBTRACTION. 

11.  From  18s.  8d.  take  13s.  lOd. 

Note. — Since  lOd.  cannot  be  taken  from  8d.,  it  be-  18s.       8d. 

comes  necessary  to  add  Is.  =  12d.  to  8d.,  making  20d.,  jcj        iq 

and  10   from  20  leaves  lOd.     Then  17s.  -  13s.  =  4s.  -— 

The  remainder  is  4s.  lOd.  ^        *-®>  Ans. 

12.  From  24  mi.  7  fur.  8  rd.  12|  ft.  take  15  mi.  6  fur.  30  rd. 
4|  feet. 

13.  From  1  lb.  take  10  oz.  17  pwt.  18  gr. 

14.  From  £2$  take  7f  shillings. 

15.  A  barrel  (31^  gal.)  is  £  full ;  if  7  gal.  are  drawn  off,  what 
part  of  the  contents  will  remain  ? 


Subtraction.  61 

157.  To  find  the  Exact  Number  of  Years,  Months,  and  Days, 
between  two  dates. 

16.  What  is  the  difference  of  time  between  Sept.  12,  1882, 
and  Dec.  25,  1884  ? 

Analysis.— The  time  from  Sept.  12, 1882,  to  Sept.  12,  1884  =  2  yr. 
The  time  from  Sept.  12th  to  Dec.  12th  =  3  mo. 

The  time  from  Dec.  12th  to  Dec.  25th  =13  d. 

Ans.  2  yr.  3  mo.  13  d.     Hence,  the 

Eule. — First  find  the  number  of  entire  years,  next  the 
number  of  entire  months  remaining,  then  the  days  in 
the  parts  of  a  month. 

Note. — 1.  The  day  on  which  a  note  or  draft  is  dated,  and  that  on 
which  it  becomes  due,  must  not  both  be  reckoned.  It  is  customary  to  omit 
the  former  and  count  the  latter. 

17.  How  much  time  between  Nov.  10,  1876,  and  May  15, 
1883? 

18.  A  note  dated  Dec.  12,  1871,  was  paid  Oct.  1,  1884 ;  how 
long  did  it  run  ? 

19.  Wellington  was  born  May  1,  1769  ;  how  old  was  he  at 
the  date  of  the  battle  of  Waterloo,  which  occurred  June  18, 
1815? 

20.  Find  the  exact  number  of  days  between  Apr.  10,  1879, 
and  Aug.  25,  1880. 

Note.— 2.  In  finding  the  operation. 

exact  time  by  days,  write       Apr.  10,  '79  to  Apr.  10,  '80  =  365  d. 

down  365  d.    as  the  time       Apr.  30-10  =     20  d. 

May  has  -    31  d. 

June    <•'  30  d. 

days  remaining  in  the  first  "uty  «H  ". 

and  each  succeeding  month ;  Aug.     "  25  d. 

the  sum  is  the  number  of  An S    502  d 

days  required. 

21.  How  many  days  did  a  note  run  dated  June  1,  1879,  and 
paid  Sept.  28,  1880  ? 

22.  How  many  days  from  June  13,  1869,  to  Sept.  30  fol- 
lowing ? 


from  the  first  date  to  the 
same  date  the  next  year 
then  write  in  a  column  the 


62  Compound  Numbers. 

23.  From  May  6,  '81,  to  Aug.  11,  '82  ? 

24.  From  Apr.  24,  '82,  to  July  4,  '83  ? 

25.  From  Jan.  28,  '75,  to  Feb.  6,  '76  ? 

26.  From  Dec.  25,  '82,  to  Jan.  31,  '83  ? 

27.  The  latitude  .of  Cape  Cod  is  42°  1'  57"  N.,  that  of  New 
York  is  40°  42'  43";  what  is  the  difference  of  their  latitude? 

Note. — 3.  When  two  places  are  on  opposite  sides  of  the  Equator,  the 
difference  of  latitude  is  found  by  adding  their  latitudes. 

28.  The  latitude  of  Havana  is  23°  9'  N.,  that  of  Cape  Horn 
is  55°  59'  S. ;  what  is  the  difference  ? 

29.  The  latitude  of  Valparaiso  is  33°  2'  S.,  that  of  St.  Au- 
gustine is  29°  48'  30"  N. ;  what  is  the  difference  ? 


MULTIPLICATION. 
158.     l.  Multiply  2  lb.  8  oz.  5|  pwt.  4  gr.  by  8. 

Explanation.— Multiply  each  2  lb.  8  oz.  5|  pwt.  4  gr. 

denomination  separately  and  unite  %                                    g 

like  denominations  as  in  addition. 

Or  the  multiplicand  may  be  reduced      Ans-  21  lb-  6  oz-     5  Pwt-  8  gr- 
to  the  decimal  of  a  pound  by  Art.  154. 

Note. — If  a  fraction  occurs  in  the  product  of  any  denomination  except 
the  lowest,  it  should  be  reduced  to  lower  denominations,  and  be  united  to 
those  of  the  same  name  as  in  Compound  Addition.     (Art.  156.) 

2.  Multiply  £12  8s.  6d.  by  6. 

3.  Multiply  17  gal.  3  qt.  1  pt.  2  gi.  by  8. 

4.  Multiply  48  mi.  3  fur.  10  rd.  by  12. 

5.  Multiply  2  hr.  45  min.  17  sec.  by  25. 

6.  Multiply  48°  25'  17"  by  28. 

7.  Multiply  28  bu.  6  pk.  5  qt.  by  13. 

8.  Of  36  persons  visiting  the  Crystal  Palace,  London,  17 
spent  16s.  lfd.  apiece;  each  of  the  rest  spent  8s.  10-Jd,  more 
than  each  of  the  17  5  how  much  did  they  all  spend  ? 


Longitude.  63 


DIVISION. 

159.  9.  A  man  paid  £15  12s.  6^d.  for  8  chests  of  tea ; 
what  was  that  a  chest  ? 

Note.— Since  8  chests  cost  £15  12s.  operation. 

6Jd.,  1  chest  will  cost  j  as  much,  and  8  )  £15   12s.  6^d. 

£15+8  =  £1,  and  £7  over.     Reducing       An§     £±   19g      Q(L  g,  far> 
£7  to  shillings  and  adding  the  12s.  gives 

152s.,  which  divided  by  8  is  19s.     The  pence  cannot  he  divided  by  8,  but 
6£  d.  =  25  far.,  which +8  =  3^  far.    Am.  £1  19s.  3±  far. 

10.  Divide  12  gal.  3^  qt.  by  5.         12.   18s.  3£d.-r-5  ==  ? 

11.  Divide  24  bu.  3|  pk.  by  7.  13.  83°  19'  9"-f-15  =  ? 

14.  How  many  cords  in  a  pile  of  wood  196  ft.  long,  7  ft. 
6  in.  high,  and  8  ft.  wide  ? 

15.  Paid  £1  7s.  7Jd.  for  a  boy's  coat  and  vest ;  the  price  of 
the  coat  was  double  that  of  the  vest ;  what  price  was  the  vest  ? 

16.  If  a  franc  is  $.193,  how  many  francs  equal  $1500  ? 

17.  An  importer  paid  £48  7s.  3d.  for  English  files,  at  £1 
6s.  6d.  per  dozen ;  how  many  dozen  did  he  import  ? 

18.  If  a  rail-car  goes  17  mi.  in  45  min.,  how  far  will  it  go  in 
5  hr.  at  the  same  rate  ?  • 

19.  In  4  mi.  3  fur.  28  rd.  4  yd.,  how  many  kilometers  ? 

LONGITUDE. 

160.  The  Longitude  of  a  place  is  the  number  of  deg.,  min., 
and  sec,  reckoned  on  the  equator,  between  a  standard  meridian 
(marked  0°)  and  the  meridian  of  the  given  place. 

All  places  are  in  East  or  West  longitude,  according  as  they 
are  East  or  West  of  the  Standard  Meridian,  until  180°,  or  half 
the  circumference  of  the  Earth  is  reached. 

Notes. — 1.  The  English  reckon  longitude  from  the  meridian  of  Green- 
wich ;  the  French  from  that  of  Paris.  Americans  generally  reckon  it  from 
the  meridian  of  Greenwich  ;  sometimes  from  that  of  Washington. 

2.  When  two  places  are  on  opposite  sides  of  the  Standard  Meridian, 
the  difference  of  Ion.  is  found  by  adding  their  longitudes.    (Art.  157,  N(.  3.) 


64  Compound  Numbers. 

161.  Comparison  of  Longitude  and  Time. 

162.  The  Earth  turns  on  its  axis  once  in  24  hours  ;  hence, 
■fa  part  of  360°,  or  15°  of  longitude,  passes  under  the  sun  in 
1  hour. 

Again,  -fa  of  15°  Ion.,  or  15',  passes  under  the  sun  in  1  min. 
of  time.  And  -fa  of  15',  or  15"  Ion.,  passes  under  the  sun  in 
1  sec.  of  time,  as  seen  in  the  following 

Table. 

360°  Ion.  make  a  difference  of  24  hrs.  of  time. 
15°         «  "  «  lhr. 

"         4  mm. 
1'         "  "  "  4  sec. 

1"       "  "  "       TVsec. 

163.  To  find  the  difference  of  Longitude  between  two  places, 
the  difference  of  Time  being  known. 

1.  The  difference  of  time  between  St.  Petersburg  and  Wash- 
ington is  7  hr.  9  min.  19£  sec.  What  is  the  difference  of 
longitude  ? 

Explanation.  —  Every    15'   of   Ion.  operation. 

makes  a  difference  of  1  min.  of  time  ;  7  hr.  9  mill.  19 J  sec. 

hence  there  must  be  15  times  as  many  15 

min.   of    Ion.    as   there    are    min.    and  „ 

seconds  of  time,  and  (7  hr.  9  min.  19£  sec.)         Ans'  iU7      iy     4y* 
x  15  =  107°  19'  48f".    Hence,  the 

Kule. — Multiply  the  difference  of  time,  ex-pressed  in 
hours,  minutes,  and  seconds,  by  15 ;  the  product  will  be 
the  difference  of  longitude  in  degrees,  minutes,  and 
seconds.     (Art.  162.) 

2.  A  ship  sailing  westward  reached  a  point  where  its  chro- 
nometer at  noon  showed  the  time  at  Greenwich  to  be  6  hr. 
45  min.  28  sec,  p.  M. ;  what  was  its  longitude  ? 

3.  If  the  difference  of  time  between  two  places  is  19  min. 
12  sec,  what  is  the  difference  of  longitude  ? 

4.  The  difference  of  time  between  New  York  and  Chicago  is 
54  min,  30J-  sec     What  is  the  difference  of  longitude  ? 


Longitude.  65 

5.  If  the  time  at  Greenwich  is  4  hr.  56  min.  4^  sec.  when 
it  is  noon  at  New  York,  what  is  the  difference  of  longitude  ? 

164.  To  find  the  Difference  of  Time  between  two  places,  the 
Difference  of  Longitude  being  known. 

6.  When  it  is  2  hr.  36  min.,  A.  m.,  at  Cape  of  Good  Hope,  Ion. 
18°  24'  E.,  what  is  the  time  at  Cape  Horn,  Ion.  67°  21'  AY.  ? 

Explanation.— The  difference  of  longitude  18°     24'  E. 

between    two    places   on   opposite   sides   of  the  g^°      21'  W. 

standard  meridian  is  found  by  adding  their  Ion-  — • 

gitudes.     As  there  are  ^  as  many  hrs.,  etc.,  as  -^  /  "^        ^   ^l^ 

there  are  deg.,  the  difference  of  time  is  5  hr.  43  min.  Ans.  5  hr.  43  min. 

Again,  12  hr.—  5  hr.  43  min.  =  6  hr.  17  min. 
Adding  to  this  the  time  before  12,        2         36 
Gives  the  hour  before  midnight.  8  hr.  53  min.,  Ans. 

Hence,  the 

Eule. — Divide  the  difference  of  longitude,  in  degrees, 
minutes,  and  seconds,  by  15 ;  the  quotient  will  be  the 
difference  of  time  in  hours,  minutes,  and  seconds. 

Note. — Add  the  difference  of  time  for  places  east,  and  subtract  it  for 
places  icest  of  a  given  meridian. 

7.  New  York  being  3°  E.  from  Washington,  and  San  Fran- 
cisco 45°  25'  W.,  what  time  will  it  be  at  New  York  when  it  is 
noon  at  San  Francisco  ? 

8.  The  difference  of  Ion.  between  Albany  and  San  Fran- 
cisco is  48°  41'  55"  ;  what  is  the  difference  of  time  ? 

9.  Constantinople  is  in  Ion.  28°  49'  E.,  St.  Paul  93°  4'  55" 
W. ;  when  it  is  2  o'clock  p.  m.  at  St.  Paul,  what  time  is  it  at  the 
former  place  ? 

io.  Mobile,  Ala.,  is  88°  1'  29"  W.  Ion. ;  Cambridge,  Eng.,  is 
5'  2"  E.  Ion.  When  it  is  noon  at  Mobile,  what  time  is  it  at 
Cambridge  ? 

n.  How  much  earlier  does  the  sun  rise  in  Boston,  Ion.  71° 
3'  30",  than  in  New  Orleans,  Ion.  90°  2'  30"  ? 

12.  Than  in  Astoria,  Ion.  124°  ?     St,  Louis,  90°  15'  15"? 

13.  Than  in  Chicago,  Ion.  87°  37'  45"  ? 

5 


66 


Weights  and  Measures. 


APPLICATION    OF    WEIGHTS    AND 
MEASURES. 


^AD- 


MEASUREMENT    OF     SURFACES. 
165.  A  Surface  is  that  which  has  length  and  breadth  only. 


166.  An  Angle  is  the  opening  between 
two  lines  which  meet  at  a  point,  as  BAC. 

The  Lines  AB  and  AC  are  called  the 
sides ;  and  the  Point  A,  at  which  they 
meet,  the  Vertex  of  the  angle. 

167.  When  two  straight  lines  meet  so 
as  to  make  the  two  adjacent  angles  equal, 
the  lines  are  Perpendicular  to  each  other, 
and  the  two  angles  thus  formed  are  called 
Right  Angles;  as,  ABC,  ABD. 

168.  A  Plane  Figure  is  one  which  repre- 
sents a  plane  or  flat  surface. 

169.  The  Perimeter  of  a  plane  figure  is 
the  line  which  bounds  it. 


170.  The  Area  of  a  plane  figure  is  the  quantity  of  surface  it 
contains. 

171.  The  Dimensions  of  a  plane  figure  are  its  length  and 
breadth. 

172.  A  Rectangle  is  a  plane  figure  having  four  sides  and 
four  right-angles.     (Art.  168.) 

173.  When  all  the  sides  of  a  rectangle  are  equal,  it  is  called 
a  Square. 

174.  When  its  opposite  sides  only  are  equal,  it  is  called  a 
Parallelogram, 


Measurement  of  Surfaces.  67 

175.  The  measuring  unit  of  surfaces  is  a  Square,  each  side 
of  which  is  a  linear  unit. 

176.  To  find  the  Area  of  Rectangular  Surfaces. 

1.  How  many  square  rods  in  a  field  28  rods  long  and 
12  rods  wide  ? 

Solution. — A  rectangle  28  rods  long   and  opekation. 

1  rod   wide   will  contain   28  sq.  rods.     And   a  28  rods, 

field  28  rods  long  and  12  rods  wide   will   con-  -j  o 

tain    12   times   28,    or  336   square  rods,   Ans.  

Hence,  the  An^  336  sq.  rods. 

V 

Kule. — Multiply  the  length  by  the  bj^eadth. 

(  1.  Area  =  Length  x  Breadth. 

Formulas. —  •<  2.  Length  =  Area  -^  Breadth. 

(  3.  Breadth  =  Area  -+■  Length. 

Notes. — 1.  Both  dimensions  should  be  reduced  to  the  same  denomina- 
tion before  they  are  multiplied. 

2.  One  line  is  said  to  be  multiplied  by  another,  when  the  number  of 
units  in  the  former  are  taken  as  many  times  as  there  are  like  units  in  the 
latter.     (Art.  10,  2°.) 

2.  Bought  a  rectangular  farm  245  rods  long  and  88  rods 
wide,  at  $75  per  acre  ;  what  was  the  cost  ? 

3.  How  many  yards  of  carpeting,  27  in.  wide,  will  be  required 
to  cover  a  floor  22  ft.  long  and  15  ft.  wide  ? 

Note. — This  and  similar  examples  admit  of  two  answers,  each  of 
which  is  correct ;  the  one  in  a  mathematical  sense,  the  other  in  a  com- 
mercial sense.  1st.  There  are  36|  sq.  yds.  in  the  floor;  to  cover  this 
requires  48f  yards  of  carpeting,  27  in.  wide. 

2d.  The  exact  number  of  sq.  feet  in  a  floor  does  not  always  correspond 
with  the  quantity  of  carpeting  which  must  be  bought  to  cover  it. 

Since  6|  breadths,  3  qrs.  wide  and  7^  yds.  long,  are  required  to  cover 
the  floor,  and  the  fractional  breadth  must  be  as  long  as  any  other,  it  will 
be  necessary  to  buy  7  times  7|  yds.  =  51^  yards. 

4.  A  building  lot  is  150  ft.  front  and  contains  2  A. ;  how 
far  back  does  it  extend  ? 


68  Weights  and  Measures. 

5.  A  man  bought  a  rectangular  field  containing  3750  sq. 
rods,  the  length  of  which  was  75  rods,  at  $15  per  acre ;  what 
was  its  breadth  and  what  did  it  cost? 

6.  How  many  rolls  of  paper  25  ft.  long  and  18  in.  wide  will 
be  required  to  cover  a  wall  26  ft.  long  and  13  ft.  high? 

7.  What  will  it  cost  to  concrete  a  court  that  is  268  ft.  square, 
at  $3.86  per  sq.  yard  ? 

8.  How  many  sq.  inches  in  a  flat  roof  54  ft.  long  and  25  ft. 
wide? 

177.  To  find  the  Area  of  an  Oblique-angled  Parallelogram,  the 
Length  and  Altitude  being  given. 

Multiply  the  length  by  the  altitude. 

Note. — If  the  area  and.  altitude,  or  one  side  are  given,  the  other  factor 
is  found  by  dividing  the  area  by  the  given  factor.    (Art.  30,  3°.) 

9.  What  is  the  area  of  an  oblique-angled  parallelogram 
whose  length  is  60  ft.  and  its  altitude  53  feet  ? 

Ans.  3180  sq.  feet. 

10.  A  grove  in  the  form  of  an  oblique-angled  parallelogram 
contains  80  acres,  and  the  length  of  one  side  is  160  rods;  what 
is  its  width  ? 

Note. — The  area  of  a  square,  a  rectangle,  a  rhomboid  and  rhombus  is 
found  in  the  same  manner. 

11.  How  many  sq.  feet  in  a  piece  of  land  13  rods  square? 

12.  One  side  of  an  acre  of  land  in  shape  of  a  rectangle  is  9 
rods  long  ;  what  is  the  length  of  the  other  side  ? 

13.  What  cost  a  field  77  rd.  long  and  41  rd.  wide,  at  $18.60 
an  acre  ? 

178.  To  find  the  Area  of  a  Trapezoid,  when  its  Parallel  Sides 
and  Altitude  are  given. 

14.  The  parallel  sides  of  a  trapezoid  are  26  ft.  and  38  ft.,  and 
its  altitude  14  ft. ;  find  its  area  ? 

Solution.— The  sum  of  the  parallel  sides  26  +  38  =  64  ft. ;  \  of  64  = 
32  ft.,  and  32  x  14  =  448  sq.  ft.,  Ans.     Hence,  the 


Measurement  of  Rectangular  Bodies.  69 

Rule. — Multiply  half  the  sum  of  the  parallel  sides  by 
the  altitude. 

15.  What  is  the  area  of  a  board  13  in.  wide,  one  side  of 
which  is  24  in.,  the  other  28  inches  ? 

16.  The  two  parallel  sides  of  a  field  are  85  and  90  rods,  and 
the  distance  between  them  54  rods ;  how  many  acres  were 
there  ? 


MEASUREMENT     OF      RECTANG-ULAR 
BODIES. 

179.  A  Rectangular  Body  is  one  bounded  by  six  rectangular 
sides,  each  opposite  pair  being  equal  and  parallel ;  as,  boxes  of 
goods,  blocks  of  hewn  stone,  etc. 

180.  When  all  the  sides  are  equal,  it  is  a  Cube ;  when  the 
opposite  sides  only  are  equal,  it  is  a  Parallelopiped. 

181.  The  Contents  or  Volume  of  a  body  is  the  quantity  of 
matter  or  space  it  contains. 

182.  The  Dimensions  of  a  rectangular  body  are  its  length, 
breadth,  and  thickness. 

183.  To  find  the  contents  op  volume  of  Rectangular  Bodies. 

l.  How  many  cu.  ft.  in  a  box  of  goods  4  ft.  long,  3  ft.  wide, 
and  2  ft.  thick  ? 

Solution. — Since  the  box  is  4  ft.  long  and 
3  ft.  wide,  there  are  12  sq.  ft.  in  the  upper  face. 
If  the  box  were  1  ft.  thick  it  must  have  as 
many  cu.  ft.  as  there  are  sq.  ft.  in  the  upper 
face.  But  it  is  2  ft.  thick  and  therefore  con- 
tains (4  x  3)  x  2  =  24  cu.  feet,  Ans.     Hence,  the 

Rule. — Multiply  the  length,  breadth,  and  thickness 
together.     (Art.  30,  3°.) 

Notes. — 1.  When  the  contents  and  two  dimensions  are  given,  the 
other  dimension  may  be  found  by  dividing  the  contents  by  the  product  of 
the  two  given  dimensions.     (Art.  30,  3°.) 


y  y  y  y  a 

> /^j 

I  ji.n.1        1,      |-||: 

n^i7Fpr 

70  Weights  and  Measures. 

2.  Excavations  and  embankments  are  estimated  by  the  cubic  yard.  In 
removing  earth,  a  cu.  yard  is  called  a  load. 

2.  What  will  it  cost  to  dig  a  cellar  40  ft.  long,  32  ft.  wide, 
and  8  ft.  deep,  at  25  cts.  a  cubic  yard  ? 

3.  How  many  cu.  meters  in  a  mound  whose  length,  breadth, 
and  height  are  each  6.4  meters  ? 

4.  How  many  loads  of  earth  must  be  removed  in  digging  a 
cellar  40  ft.  long,  20  ft.  wide,  and  8  ft.  deep  ? 

5.  How  many  cu.  ft.  in  10  boxes,  each  7|  ft.  long,  If  ft. 
wide,  and  1J-  ft.  high  ? 

CISTERNS,     BINS,     ETC. 

184.  The  Capacity  of  rectangular  cisterns,  bins,  etc.,  is 
measured  by  cubic  measure,  but  the  results  are  commonly 
expressed  in  units  of  Liquid  and  Dry  Measure. 

185.  To  find  the  Number  of  Gallons  in  Rectangular  Cisterns,  etc. 

6.  How  many  gallons  will  a  rectangular  vat  6  ft.  long,  5  ft. 
wide,  and  4  ft.  deep  contain  ? 

Solution.— The  product  of  6  ft.  x  5  x  4  =  120  cu.  feet ;  and  120  x 
1728  =  207360  cu.  inches.  Again,  in  1  gallon  there  are  231  cu.  inches, 
and  207360-^-231  =  897f*  gal.,  Ans.     (Art.  69.) 

7.  How  many  bushels  will  a  box  8  ft.  long,  4  ft.  wide  and 
3  ft.  high  contain? 

Solution.— 8  x  4  x  3  =  96  cu.  ft.  and  96  x  1728  =  165888  cu.  in.  Since 
2150.4  cu.  in.=:  1  bu.,  165888  cu. in.  =  165888^-2150.4  =  77$  bushels.,  Ans. 
Hence,  the 

Eule. — Find  the  number  of  cubic  inches  in  the  object 
measured,  and  reduce  them  to  liquid  or  dry  measure,  as 
may  be  required.     (Arts.  69,  71.) 

8.  How  many  gallons  would  a  cistern  7  ft.  long  by  6  ft. 
wide  and  11  ft.  deep  contain  ? 

9.  At  30  cts.  a  square  yd.,  what  would  be  the  cost  of  plaster- 
ing the  bottom  and  sides  of  such  a  cistern  ? 


Measurement  of  Lumber.  71 

10.  If  a  reservoir  45  ft.  long,  28  ft  wide,  contains  45360  hhd., 
how  high  must  it  be  ? 

n.  At  $1.12!  a  bushel,  what  is  the  value  of  a  bin  of  wheat 
9  ft.  long,  7  ft.  wide,  and  4  ft.  deep  ? 

12.  A  farmer  had  a  bin  8  ft.  long,  4£  ft.  wide,  and  2£  ft. 
deep,  which  held  67|  bu.;  how  deep  should  another  bin  be 
made  which  is  16  ft.  long,  4£  ft.  wide,  that  its  capacity  may  be 
460  bushels  ? 

13.  How  many  hogsheads  of  water  will  a  cistern  hold,  which 
is  5  ft.  6  in.  square  and  8  ft.  deep  ? 

MEASUREMENT     OF    LUMBER. 

186.  A  standard  Board  Foot  is  1  ft.  long,  1  ft.  wide,  and  1 
in.  thick ;  that  is,  a  square  foot  1  inch  thick.  Hence, 
A  Cubic  Foot  is  equal  to  12  board  feet. 

187.  A  Board  Inch  is  TV  of  a  board  foot ;  that  is,  1  inch 
long  by  12  inches  wide  and  1  inch  thick.  Hence,  Twelve 
board  inches  are  equal  to  1  board  foot. 

188.  Sawed  timber,  as  plank,  joists,  etc.,  is  estimated  by 
cu.  feet ;  hewn  timber,  as  beams,  etc.,  either  by  board  feet  or 
cu.  feet;  round  timber,  as  masts,  etc.,  by  cu.  feet. 

189.  To  find  the  Contents  of  Boards,  Planks,  etc. 

1.  How  many  board  feet  in  a  board  13  ft.  long,  18  in.  wide, 
and  1  inch  thick  ? 

Explanation. —  Multiplying    the    length  operation. 

in  feet  by  the  width  and  thickness  expressed  13  X  18  X  1  =■  234  in. 

in  inches,  we  have  234  board  inches.     Divid-  234-^12  =  19i  ft. 

ing  this  product  by  12,  the  result  is  19.1  board  .         i qi  -Pf 

feet,  Ans.  MS'    L^  U' 

2.  How  many  board  feet  in  a  scantling  14  ft.  long,  6  in. 
wide,  and  &|  in.  thick  ? 

Solution.— Multiplying  the  length  in  feet  by  the  width  and  thickness 
expressed  in  inches,  we  have  14x6x2§  =  210  in.,  and  210 + 12  =  17£ 
board  ft.,  Ans.     Hence,  the 


72  Weights  and  Measures. 

Rule. — Multiply  the  length  in  feet  by  the  width  and 
thickness  expressed  in  inches,  and  divide  the  product  by 
12  ;  the  quotient  will  be  in  board  feet. 

Notes. — 1.  The  standard  thickness  of  a  board  is  1  inch.  If  less  than 
1  inch,  it  is  disregarded  ;  if  more  than  1  inch,  it  becomes  a  factor  in  find- 
ing the  contents  of  plank,  scantling,  etc. 

If  one  of  the  dimensions  is  inches,  and  the  other  two  are  feet,  the 
'product  will  be  in  Board  feet. 

2.  If  a  board  is  tapering,  multiply  the  length  by  half  the  sum  of  the 
two  ends 

3.  The  approximate  contents  of  round  timber  or  logs  may  be  found  by 
multiplying  |  of  the  mean  circumference  by  itself,  and  this  product  by  the 
length. 

3.  How  many  feet  in  a  board  14  ft.  long  and  18  in.  wide, 
and  of  standard  thickness  ? 

4.  Find  the  contents  of  a  tapering  board  15  ft.  long,  16  in. 
wide  at  one  end  and  11  in.  at  the  other  ? 

5.  What  cost  125  boards  11  ft.  long,  and  15  in.  wide,  at  4£ 
cents  a  board  foot  ? 

6.  What  cost  28  joists  whose  dimensions  are  4  in.  by  3J  in. 
and  11  ft.  long,  at  25  cts.  a  cu.  foot? 

7.  How  many  cu.  feet  in  a  log  65  ft.  long,  whose  mean 
circumference  is  12  ft.  ? 

8.  How  many  cu.  ft.  in  a  beam  24  ft.  6  in.  long,  1  ft.  9  in. 
wide,  and  1  ft.  2J  in.  thick  ? 

9.  How  many  feet  of  boards  would  be  required  to  build  a 
fence  4  ft.  high  and  126  ft.  long,  and  what  would  be  the 
expense  at  $2£  for  100  feet? 

10.  What  cost  a  ship's  mast  56  ft.  long  and  9  ft.  in  circum- 
ference, at  $1. 12 J  per  cu.  foot  ? 

11.  How  many  boards  12  ft.  long  and  4  in.  wide  are  required 
for  a  floor  36  ft.  by  27  ft.  ? 

12.  How  many  feet  of  boards  would  be  needed  to  make  9 
piano  boxes,  the  interior  dimensions  of  which  are  6  ft.  8  in., 
5  ft.  7  in.,  and  3  ft.  6  in.  respectively,  the  boards  being  1 J  in. 
thick  ? 


Masonry.  73 


MASONRY. 

190.  Stone  Masonry  is  usually  estimated  by  the  perch ; 
Brickwork  by  the  thousand  bricks. 

Notes. — 1.  A  perch  of  stone  masonry  is  16|  ft.  long,  \\  ft.  wide,  and 
1  ft.  high,  which  is  equal  to  2  4  J  cu.  ft.  It  is  customary,  however,  to  call 
25  cu.  ft.  a  perch. 

2.  The  average  size  of  bricks  is  8  in.  long,  4  in.  wide,  and  2  in.  thick. 

In  estimating  the  labor  of  brickwork  by  cu.  feet,  it  is  customary  to 
measure  the  length  of  each  wall  on  the  outside  ;  no  allowance  being  made 
for  windows,  doors,  or  corners.  But  a  deduction  of  ^  the  solid  contents 
is  made  for  the  mortar. 

1.  In  the  walls  of  a  cellar,  the  thickness  of  which  is  1  ft.  6  in., 
the  height  8  ft.,  each  side  wall  52  ft.,  and  each  end  wall  25 
ft. ;  how.  many  perch  (25  cu.  ft.)  ? 

2.  At  I4.87J  a  perch,  what  will  it  cost  to  build  the  walls  of 
the  above  cellar  ? 

3.  How  many  bricks  are  required  for  a  building  the  walls 
of  which  are  58  ft.  long,  25  ft.  wide,  44  ft.  high,  and  1  ft.  thick, 
making  no  allowance  for  windows,  doors,  corners,  or  mortar  ? 

4.  At  $3.75  per  M.  for  bricks,  and  $4.25  per  M.  for  laying 
them,  deducting  ^  for  mortar,  what  will  the  walls  of  such  a 
building  cost? 


APPLICATIONS    OF    UNITED    STATES 
MONEY. 

191.  United  States  Money  is  added,  subtracted,  multiplied, 
and  divided  like  Decimal  Fractions,  and  requires  no  special 
rules. 

1.  A  man  has  farms  valued  at  $56850,  city  lots  at  $86960,  a 
house  worth  $12800,  and  other  property  $8750  ;  what  is  the 
whole  worth?  Ans.  $165360. 

2.  If  a  student's  expenses  are  $198  for  board,  $37.50  for 
clothes,  $150  for  tuition,  $35.87  for  books,  $27.37£  for  inci- 


74  United  States  Money. 

dentals,  annually,  what  would  it  cost  a  year  to  educate  4  boys 
at  the  same  rate  ? 

3.  The  cost  of  laying  the  Atlantic  Cable  was  as  follows : 
2500  mi.,  at  $485  per  mile ;  10  mi.  deep  sea  cable,  at  $1450 ; 
25  mi.  shore  ends,  at  $1250 ;  what  was  the  whole  cost  ? 

4.  Bought  wheat  at  94  cts.  a  bushel  to  the  amount  of 
$59.22,  and  sold  for  $70.56;  what  was  the  selling  price  per 
bushel  ? 

5.  In  selling  86.55  tons  of  coal,  at  $5. 64  per  ton,  a  merchant 
made  $100.63  ;  how  much  did  it  cost  him  a  ton  ? 

6.  Paid  $2225  for  180  sheep,  and  sold  them  for  $2675  ;  what 
should  I  gain  on  1500  sheep  at  the  same  rate  ? 

7.  A  man  bought  an  acre  of  land  for  $1250 ;  he  afterwards 
sold  100  ft.  square  for  $1000,  and  divided  the  remainder  into 
lots  of  25  x  100  ft.,  which  were  sold  at  $500  each  ;  how  many 
lots  did  he  sell,  and  how  much  did  he  make  in  the  transaction  ? 


METHODS    BY    ALIQUOT    PARTS. 

50    cts.  =  $4.  12J  cts.  s=  $4.  40    cts.  ss  $| 

334  cts.  =  $f  10    cts.  ss  $1l  37J  cts.  =  $| 

25     cts.  sa  $J.  Si  cts.  =  $TV  62J  cts.  =  ! 

20    cts.  ss  $-§.  6£  cts.  =  $^g-.  75     cts.  =  I 

16 1  cts.  =  $f  5     cts.  s=  $^.  87 J-  cts.  =  I 

192.  To  find  the  Cost  of  a  number  of  like  things,  when  the 
Price  of  one  is  an  Aliquot  Part  of  $1. 

8.  At  33 J  cts.  each,  what  cost  576  Grammars? 

Analysis.— At  $1  each  they  would  cost  $576;  but  the  3  )  576 

price  is  33J  cts.  =  $^,  and  576-J-3,  or  x|  =  192.    Hence,  the    jins.  $192 

Eule. — Multiply  the  given  number  of  things  by  the 
fractional  part  of  $1  which  expresses  the  price  of  One; 
the  result  is  the  cost.     (Complete  Grad.  Arith.,  Art.  208.) 

9.  What  cost  17  chests  of  tea  of  59  lbs.  each,  at  33|  cts.  a 
pound  ? 


Aliquot  Parts.  75 

10.  Sold  18  bbl.  pork  of  200  lb.  each,  at  12£  cts.  a  pound ; 
what  did  it  come  to  ? 

11.  Find  the  cost  of  158  tons  coal,  at  $5.33£  a  ton. 

12.  170  lb.  soap,  at  8 J  cts.  a  pound. 

13.  264  lb.  raisins,  at  25  cts.  a  pound. 

14.  295  lb.  8  oz.  butter,  at  33|  cts.  a  pound. 

15.  756  yd.  calico,  at  20  cts.  a  yard. 

16.  275  doz.  eggs,  at  12£  cts.  a  dozen. 

17.  1260  pine  apples,  at  16f  cts.  a  piece. 

18.  What  cost  4  lb.  5  oz.  6  pwt.  of  gold  dust,  at  75  cts.  a 
pennyweight  ? 

19.  A  man  gave  87-J  cts.  a  sq.  rd.  for  503  A.  of  land;  what 
did  it  cost  him  ? 

20.  What  would  be  the  cost  of  enclosing  a  square  lot  of  160 
acres  with  a  fence  costing  75  cts.  a  yard  ?    (Art.  621.) 

193.   To  find  the  Number  of  Like  Tilings  when  their  Cost 
is  given,  and  the  Price  of  One  is  an  Aliquot  Part  of  $1. 

21.  How  many  pounds  of  coffee  at  33J  cts.  a  pound  can  be 
bought  for  $84.50? 

Analysis. — Since  the  price  is  %\  a  operation. 

pound,    $1   will    buy   3  pounds,  and  $0.33^  =  $J 

$84.50  will  buy  84.50  x  3  =  253.5  lb.  84  50  x  3  =  253  5 

Or,  at  §1  a  pound    $84.50  will  buy  as        Qr  m/5Q^$i  _  gg^g  lb. 
many  pounds  as  $|  is  contained  times  6 

in  $84.50,  or  253.5  pounds,  Ans.    Hence,  the 

Rule. — Divide  the  cost  of  the  whole  by  the  aliquot  part 
of  $1  ivhich  is  the  price  of  One. 

22.  How  many  lb.  butter  at  33-J-  cts.  can  be  bought  for  56  lb. 
tea,  at  62£  cts. 

23.  What  cost  3  bu.  2  pk.  3  qt.  of  peas,  at  87J-  cts.  a  peck  ? 

24.  If  a  man  can  pay  62-J  cts.  on  a  dollar,  how  much  can  he 
pay  with  $1352.50  ? 


76  United  States  Money. 

25.  Bought  14  bbl.  salt  of  4  bu.  each,  at  $1.40  a  barrel,  and 
sold  it  at  10  cts.  a  peck ;  what  was  the  gain  ? 

26.  At  6J  cts.  a  foot,  how  many  planks  each  measuring  26  ft. 
9  in.,  can  be  bought  for  $36.78£? 

27.  How  many  bales  of  cotton  of  450  lb.  each,  at  37J  cts.  a 
pound,  are  equal  in  value  to  15  hhd.  sugar  of  1800  lb.  each,  at 
8-J  cts.  a  pound  ? 

194.  To  find  the  Cost  of  a  number  of  articles,  the  Price  of 
one  being  $1  plus  an  Aliquot  part  of  $1. 

28.  At  $1.25  a  bu.,  what  cost  568  bushels  of  wheat  ? 

Analysis.— At  $1  a  bu.,  the  cost  would  be  $568.       4  )  ^68 
But  the  price  is  $1£,  therefore  568  bu.  will  cost  568+  142 

143  (i  of  568)  =  $710.     Hence,  the  |^10    j_ngt 

Rule. — To  the  number  of  articles,  add  its  proper  frac- 
tional part ;  the  sum  will  be  their  cost. 

29.  At  I1.37J-  per  sq.  rd.,  what  cost  263  A.  of  land  ? 

30.  Bought  in  Michigan  300  bu.  of  oats,  at  1\  cents  a 
pound ;  what  did  they  cost  ?     (Art.  72.) 

31.  Bought  in  New  York  286440  lb.  wheat,  what  is  its  value 
at$1.87iabushel? 

195.  To  find  the  Cost,  when  the  price  per  100  or  1000  is  given. 

32.  What  cost  2925  lb.  sugar,  at  $12.50  a  hundred  ? 
Solution.— 2925  lb.=Yinr  of  100  lb.,  and  ??=Lj£—  =  $365. 62|,  Arts. 

33.  At  $4.33£  per  M.,  what  cost  2367  bricks  ? 

Solution.— The    price    per    M.  =  $4^;    then  3)2367 

(2367  x  4)  +  (2367-^3)  _  4 

looo-     --cost  ^ 

Or,  multiply  the  number  of  bricks  by  4,  add  \  of  ~oq 

the  same  number  to  the  product,  and  divide  by  1000 

by  pointing  off  3  figures  in  the  result.     Hence,  the  $10,257 


Aliquot  Farts.  77 

Kule. — Multiply  the  price  per  hundred  or  thousand  by 
the  given  number  of  things,  and  divide  the  product  by 
100  or  1000,  as  the  case  may  require.     (Art.  10,  4°-) 

Note. — In  business  transactions,  the  letter  C  is  put  for  hundred;  and 
M  for  thousand. 

34.  What  cost  536720  bricks,  at  $8.75  per  M.? 

35.  What  cost  125268  feet  of  boards,  at  $31.25  per  thou- 
sand ? 

36.  At  $5f  per  hundred,  how  much  will  25345  pounds  of 
flour  come  to  ? 

196.  When  the  cost  of  100  or  1000  articles,  pounds,  etc. ,  is 
given,  the  price  of  one  is  found  by  simply  removing  the  decimal 
point  in  the  given  cost  or  dividend,  as  many  places  to  the  left  as 
there  are  ciphers  in  the  divisor.    (Art.  264,  Com.  Grad.  Arith.) 

37.  If  pine  boards  are  $21.63  per  1000  ft.,  what  is  that  per 
foot?  Ans.  $.02163. 

38.  Bought  wheat  in  N.  Y.  at  $3.1 2 \  a  cental ;  what  would 
6410§  bu.  cost  at  the  same  rate  ? 

39.  If  12£  cw.t.  of  sugar  cost  $140,  what  is  that  a  pound  ? 

197.  To  find  the  Cost,  when  the  price  of  a  ton  of  2000  pounds 
is  given. 

40.  What  cost  5460  pounds  of  hay  at  $8.50  per  ton  ? 

Explanation.— At  $8.50  a  pound,  5460  lb.  will  5460 

cost  $46410.     But  the  price  is  per  ton  of  2000  lb. ;  §  5q 

therefore  dividing  by  2,  and  removing  the  decimal 

point  3  places  to  the  left,  will  give   the  answer.  2000  )  46410.00 

Hence,  the  £nSm   $23,205 

Eule. — Multiply  the  price  of  1  ton  by  the  given  num 
ber  of  pounds  and  divide  the  product  by  2000. 

41.  What  is  the  freight,  at  $5.40  per  ton,  on  an  exportation 
of  9654  pounds  of  cotton  ? 

42.  Bought  26  sacks  of  wool,  weighing  560  lb.  each,  at  $26.50 
per  ton ;  what  did  it  cost  ? 


78 


United  States  Money. 


BILLS     OF     MERCHANDISE. 

198.  A  Bill  is  a  written  statement  of  goods  sold,  or  services 
rendered,  with  their  prices,  etc. 

Note. — Bills  should  always  state  the  names  of  both  parties,  the  place 
and  time  of  each  transaction,  the  name  and  price  of  each  item,  and  the 
amount. 

199.  A  Bill  is  Receipted  when  the  words  "  Received  Pay- 
ment" are  written  at  the  bottom,  and  it  is  signed  by  the 
creditor,  or  by  some  person  duly  authorized. 

Exam  ples. 
Copy  and  extend  the  following  bills : 

(l.  Bill  of  Dry  Goods.) 

Boston,  Jan.  28th,  1883. 
Mr.  James  Mitchell, 

BoH  of  W.  Starbuck  &  Co. 

(Cash  after  30  days.) 


23  yds.  silk 

15  yds.  broadcloth, 

23  yds.  cambric, 

13  doz.  buttons, 

26  skeins  sewing  silk, 

14  yds.  wadding, 
47  yds.  bl.  muslin, 
35  yds.  Can.  flannel, 
42  yds.  calico, 

12  doz.  Brooks'  cotton, 
}  doz.  fancy  hose, 
8  pr.  kid  gloves, 


@  $2.12} 
@    3.75 
@       .12} 
@      .25 
@       .06J 
@      .08 
@      .12 
@      .14 
@      .12} 
@     1.08 
@  10.00 
@     2.00 


Amount,     -    - 
Bec'd  PayH, 

W.  Starbtjck  &  Co. 


Bills  of  Merchandise. 


79 


(2.  Books.) 

Messrs.  J 

New  York,  May  15tht  1883. 

C.  Griggs  &  Co., 

To  Clark  &  Maymrd,  Dr. 

1883. 

May 

1 

For  150  U.  S.  Histories,            ©  I0.62J 
«      72  Rom.        "                    @     1.15 
"      96  Grammars,                    @      .65 
"    200  Com.  Graded  Arith.,    @       .75 
"    125  Prac.  Algebras,            @      .83 
"      65  Col.             "                 @     1.05 
"      84  Physiologies,                @    1.10 

Amount,     -    - 

Redd  PayH, 

By  Draft  on  Boston, 

Clark  &  Maynard. 

(3.  Statement  of  Account.) 

San  Francisco,  Oct.  3,  1882. 
Messrs.  Robert  Standart  &  Brother, 

In  Acct.  with  Scott  &  Merwin,  Dr. 


1882. 

June 

4 

a 

15 

July 
Aug. 
Sept. 

8 
10 
20 

July 

1 
20 

Aug. 
Sept. 

10 
25 

165  tons  R.R.  iron, 
25  cwt.  Steel  Wire, 
48  doz.  Axes, 
125  Saws, 
342  cwt.  Lead, 


$45.25 

21.50 

10.40 

3.75 

7.40 


Or. 


500bbls.  Flour,  @       5.40 

456  bu.  Wheat,  @      1.17 

Dft.  on  JSTew  York, 

112  shares  Mining  Stock,      @     75.00 

Bal.  due,     -     - 
Rec'd  PayH, 

Scott  &  Merwin, 


400 


Per  Charles  Kingsford. 


80 


United  States  Money. 


Entry     Cler  k  s     Drill. 

200.  Enter  the  following  memorandum,  made  at  Detroit, 
Mich.,  and  find  the  amount  of  the  bill : 

Mem.— A.  B.  bought  of  0.  D.,  Apr.  15th,  1883,  624  lbs.  Java 
coffee,  at  25  cts. ;  420  lbs.  green  tea,  at  75  cts. ;  648  lbs.  gran- 
ulated sugar,  at  12£  cts.;  528  lbs.  brown  do.,  at  6J  cts.; 
350  lbs.  bar-soap,  at  .05;  428  gal.  linseed  oil,  at  87|  cts. 


Common     Form 


Messrs.  A.  B., 


Detkoit,  Mich.,  Apr.  15th,  1883. 
Bought  of  C.  D. 


624  lbs.  Java  Coffee,                @  25  cts. 

420  lbs.  Green  Tea,                  @  75  cts. 

648  lbs.  Granulated  Sugar,     @  12  j-  c. 

528  lbs.  Brown              "          @  6£  c. 

350  lbs.  Bar  Soap,                    @  5  cts. 

428  gal.  Linseed  Oil,               @  87£  c. 

Amount,  -    - 

Redd  Pay% 


5.  W.  A.  Sanford,  Esq.,  of  Philadelphia,  bought,  June  3d, 
1883,  of  James  Conrad,  28  yds.  of  silk,  at  $1.75  a  yard;  42 
yds.  of  muslin,  at  56  cts. ;  16  pairs  of  cotton  hose,  at  87J  cts.; 
35  pair  of  silk  hose,  at  $2.10;  and  25  pair  of  shoes,  at  $3.25. 
What  was  the  cost  of  the  several  articles,  and  how  much  is 
due  on  his  account  ? 

6.  Holmes  &  Homer  of  Cincinnati,  bought,  July  1st,  1882, 
of  H.  W.  Morgan  &  Co.,  100  bbls.  flour,  at  $5.50  a  barrel; 
50  bbls.  pork,  at  $8.25  ;  25  bbls.  beef,  at  $9.75  ;  112  kegs  of 
lard,  at  $3.25  ;  and  25  bu.  corn,  at  74  cts.  What  was  the  cost 
of  the  several  articles,  and  how  much  is  due  on  his  account  ? 


^^r°»  ... 
EROENTAGE. 


201.  Percentage  is  the  method  of  calculating  by  hundredths, 

202.  The  term  Per  Cent  (from  the  Latin  per  and  centum), 
means  by  the  hundred,  or  simply  hundredths. 

203.  The  Rate  Per  Cent  is  the  number  of  hundredths  to  be 
found  or  taken.  It  may  be  expressed  by  the  sign  %,  by  a  deci- 
mal, or  by  a  common  fraction. 

Table. 


Sign. 

Decimal. 

Fraction. 

Sign. 

Decimal. 

Fraction 

1% 

.01 

=3 

TOO" 

i% 

.005 

—       T0~0 

5% 

.05 

= 

* 

H% 

.025 

=     A 

Wo 

.10 

= 

tV 

Wo 

.0025 

—      loo 

25% 

.25 

= 

i 

H% 

.0625 

=     A 

50% 

.50 

=s 

i 

m% 

.1875 

=     A 

75% 

.75 

= 

f 

3H% 

•33i 

=       i 

100?/ 

1.00 

= 

i 

im% 

1.125 

=     H 

204.  Since  hundredths  occupy  two  decimal  places,  every 
per  cent  requires,  at  least,  two  decimal  figures.  Hence,  if  the 
given  per  cent  is  less  that  10,  a  cipher  must  be  prefixed  to  the 
figure  denoting  it.     Thus,  %%  is  written  .02;  6%,  .06,  etc. 

Notes. — 1.  A  hundred  per  cent  of  a  number  is  equal  to  the  number 
itself;  for  }£§  is  equal  to  1. 

2.  In  expressing  per  cent,  when  the  decimal  point  is  used,  the  words 
per  cent  and  the  xigit  (</c.)  mast  be  omitted,  and  vice  versa.     Thus,  .05  de- 
notes 5  per  cent,  and  is  equal  to  y|},r  or  .;„  ;   but  ,03  per  cent  or  ,00  % 
denotes  -fa  of  jfo  and  is  equai  to  jjfa  or  ¥^, 
6 


82  Percentage. 

205.  To  read  Per  Cent,  expressed  Decimally. 

Call  the  first  two  decimal  figures  per  cent;  and  those  on  the 
right,  decimal  parts  of  1  per  cent. 

Note. — Parts  of  1  per  cent,  when  easily  reduced  to  a  common  fraction, 
are  often  read  as  such.  Thus,  .105  is  read  10  and  a  half  per  cent;  .0125  is 
read  one  and  a  quarter  per  cent. 

Read  the  following  as  rates  per  cent : 

1.  .06;  .052;  .085;  .094.  4.  .121;  .08£;  .16|;  .5775. 

2.  .012;  .174;  .0836;  .154.       5.   1.07;  2.53;  4.65;  2.338. 

3.  5.33J;  4.125;  8.0623.  6.  .1857;  .2352;  .7225. 

206.  To  change  a  Per  Cent  to  a  Common  Fraction. 

7.  Change  35%'  to  a  common  fraction. 
Solution.— 35%  =  .35  and  T^%  =  fa  Ans.     Hence,  the 

Rule.  —  Write  the  per  cent  for  the  numerator  and  100 
for  the  denominator,  and  reduce  it  to  lowest  terms. 

207.  Express  the  following  by  Com.  Frac.  in  lowest  terms : 

8.  5%.  10.     30^.  12.     50%.  14.     100$. 

9.  6%.  11.     25$.  13.     15%.  15.     125$. 

16.  To  what  common  fraction  is  6|$  equal  ? 
Analysis.-6|%  =  j&  ;  ^  x  T^  =  flfc,  or  T\,  Ans.    (Art.  203.) 

17.  What  fraction  =  5 ±%?  26J$  ?  36#g?  28^?  12^? 
10f$? 

208.  To  change  a  Common  Fraction  to  an  equivalent  Per  Cent. 

18.  What  per  cent  of  a  number  is  f  ? 

Analysis.— Every  number  is  100  %  of  itself,  hence  §  8)5.00 

of  100%  =  500 -h  800,  or  5  h-  8  =  ,62|,  or  62^  f0,  Ans.       J_ns~^ 
Hence,  the 


Percentage.  83 

£ule. — Annex  ciphers  to  the  numerator,  and  divide  it 
by  the  denominator.     (Complete  Graded  Arith.,  Art.  249.) 

19.  Change  f ■$■  to  an  equivalent  per  cent. 

Ans.  .60,  or  60^.     (Art.  208.) 

20.  H  =  ?        22.      fj  =  ?  24.      If  =  ?     .   26.      f«  =  ? 

21.  «  =  ?       23.      ,ft=?        25.      -2Vo=?     27.      iff  =  5 

209.  The  Parts  or  Elements  employed  in  calculating  per- 
centage are  the  Base,  the  Bate  per  cent,  the  Bercentage,  and 
the  Amount  or  Difference. 

210.  The  Base  is  the  number  on  which  the  percentage  is 
calculated. 

211.  The  Kate  or  Rate  per  cent  is  the  number  of  hun- 
dredths of  the  base  to  be  taken. 

212.  The  Percentage  is  the  part  of  the  base  indicated  by  the 
rate  per  cent. 

Thus,  when  it  is  said  that  4%  of  $50  is  $2,  the  base  is  $50,  the  rate  .04, 
and  the  percentage  $2. 

213.  The  Amount  is  the  sum  of  the  base  and  percentage. 

214.  The  Difference  is  the  base  less  the  percentage. 

Thus,  if  the  base  is  $75  and  the  percentage  $4,  the  amount  is  $75  +  4 
=  $79  ;  the  difference  is  $75— $4  =  $71. 

The  relation  between  these  parts  is  such,  that  if  any  two  of 
them  are  given,  the  other  three  may  be  found. 

215.  To  find  the  Percentage,  the  Base  and  Rate  being  given. 

28.   What  is  8%  of  2346  ? 

Solution. -The  Base  2346  x  .08  (rate)  =  187.68,  Percentage.  Hence, 
the 

Rule. — Multiply  the  base  by  the  rate,  expressed,  in 
decimals. 


84  Percentage. 

Formula.— Percentage  =  Base  x  Rate. 

Notes. — 1.  Finding  a  per  cent  of  a  number  is  the  same  as  finding  a 
fractional  part  of  it.     (Complete  Graded  Arith.,  Art.  208.) 

2.  When  the  rate  is  an  aliquot  part  of  100,  it  is  advisable  in  most  cases 
to  take  the  parts  of  the  base  denoted  by  the  corresponding  fraction.  Thus, 
for  88£%  take  |,  etc. 

3.  When  the  base  is  a  compound  number,  the  lower  denominations 
should  be  reduced  to  a  decimal  of  the  highest ;  or  the  whole  number  to 
the  lowest  denomination  ;  then  apply  the  rule. 

29.  What  is  5%  of  £28  10s.  lid. 

Solution.— £28  10s.  lid.  =  £28.55, 'and  £28.55 x. 05  =  £1.4275,  or  £1 
8s.  6|d.,  Ana.     (Arts.  151,  153.) 

30.  6%  of  7850  =  ?  34.  12%  of  6785  =  ? 

31.  7%  of  8375  =  ?  35.  75^  of  9863  =  ? 

32.  8%  of  5873  =  ?  36.  100%  of  6842  =  ? 

33.  9%  of  3482  =  ?  37.  \%±%  of  48  lb.  3  oz.  =  ? 

38.  8$%  of  3$  A.  16  sq.  r.  =  ? 

39.  What  is  the  difference  between  h\%  of  $800  and  §\%  of 
$1050  ? 

40.  What  is  9f %  of  275J  miles  ? 

216.   To  find  the  Hate,  the  Base  and  Percentage  being  given. 

41.  What  per  cent  of  80  is  36  ? 

Analysis.— Since  percentage  is  the  product  of  base  x  80  )  36.00  P. 
rate,  the  percentage  36-^80  (the  base)  =  .45,  the  rate.  ^^  ~  -^ 
Hence,  the 

BULB. — DUM&  the  percentage  by  the  base.  (Complete 
Graded  Arith.,  Art.  119,  a.) 

Formula.— Rate  =  Percentage  -4-  Base. 

42.  What  %  of  £28  is  16s.  ?      Ans.  2%%.     (Art.  152,  N.) 

43.  Of  $250  is- $12?  46.  Of  523  is  32? 

44.  Of  365  yd.  is  28  in.  ?  47.  Of  875  is  33|  ? 

45.  Of  500  A.  is  25  A.?  48.  Of  68  is  m? 


Percentage.  85 

49.  Of  26  lb.  9  oz.  is  12  pwt.  ?    52.  Of  83  is  8|  ? 

50.  Of  475  is  175  ?  53.  Of  75  is  2|  ? 

51.  Of  654  is  62  ?  54.  Of  99  is  9J  ? 

55.  A  man  bought  350  A.  of  land,  at  $40  an  acre,  and  sold 
part  of  it  for  $2240  at  the  same  rate  ;  what  per  cent  of  the  land 
did  he  sell  ? 

56.  An  agent  received  $67.50  for  collecting  $4500 ;  what 
per  cent  was  his  commission  ? 

57.  Bought  sugar  for  $150  and  sold  it  for  $167.50;  what 
per  cent  was  the  gain  ? 

58.  A  merchant  owes  $8250,  his  assets  are  $3240  ;  what  per 
cent  of  his  debts  can  he  pay  ? 

59.  Sold  i  A.  of  land  for  what  the  whole  cost ;  what  was  the 
per  cent  gain  ? 

60.  What  per  cent  of  365  days  are  30  days  ? 

61.  Bought  a  number  of  eggs,  and  sold  11  for  the  money 
paid  for  18  ;  what  per  cent  was  the  gain  ? 

217.   To  find  the  Base,  the  Rate  and  Percentage  being  given. 

62.  $500  equal  20%  of  what  number  ?  .20  )  $500.00  P. 

Analysis.— Since  the  percentage  $500  is  a  pro-        ^ns.   $2500  B. 
duct  of  which  the  rate  .20  is  a  factor,  $500-h.20     Or  20%  =  },  and 
=  |2500,  the  base  required.     Hence,  the  $500  -h-V  —  $2500. 

Eule. — Divide  the  percentage  by  the  rate. 

Formula. — Base  =  Percentage  -f-  Rate. 

63.  184  is  12£%  of  what  number? 

Ans.  1472.     (Complete  Grad.  Arith.,  Art.  217.) 


64. 

245  =  6%  of  ? 

70. 

$68.25  =  \%\%  of  ? 

65. 

1248  =  10$  of  ? 

71. 

£248  6s.  =  \%  of  ? 

66. 

967  =  1%  of  ? 

72. 

$250.60  =  \%  of  ? 

67. 

863  ==  33^  of  ? 

73. 

1250  =  \%  of  ? 

68. 

8721  =  6i%  of  ? 

74. 

450f  as  125%  of  ? 

69. 

7500  =  \%  of  ? 

75. 

96|  =  150^  of  ? 

86  Percentage. 

76.  Paid  $50  a  month  for  house-rent,  which  was  9$  on  the 
value  of  the  house ;  what  was  it  worth  ? 

77.  An  owner  of  a  ship  sold  25$  of  it  for  $5250 ;  what  was 
the  ship  worth  ? 

78.  A  man  paid  $150  for  insurance  on  his  house,  which  was 
2J$  on  the  sum  insured  ;  for  how  much  was  it  insured  ? 

79.  A  grocer  sold  §\  cwt.  sugar,  at  $8J  per  cwt.,  and  lost 
thereby  12$  ;  what  was  the  cost  ? 

218.  To  find  the  Base,  the  Amount  or  Difference  and  the  Rate 
being  given. 

80.  What  number  increased  by  15$  of  itself  is  4600  ? 

1  +  .15  =1.15 

Analysis.— Since  4600  -  100%  +15%,  it  must  be      -i  i  k  \  Apac)  00 

115%  of  the  number,  and  4600-^-1.15  =  4000.  >  +PUU.UU 

Ans.  4000 

81.  What  number  diminished  by  25$  of  itself  is  4560? 

Analysis.— Since  4560  =  100% -25%,  it  must  be  1  —  ,35  =  '75 
75%  of  the  number,  and  4560-=-.75  =  6080,  the  num-  .75  )  4560.00 
ber  required.     Hence,  the  j^T    qqqq 

Eule. — Divide  the  amount  by  1  increased  by  the  rate. 
Or,  Divide  the  difference  by  1  diminished  by  the  rate. 

„  d         _  i  Amount  -j-  (1  -f  Rate). 

~  \  Difference  -^  (1  —  Rate). 

What  number  plus  What  number  minus 

82.  12f$  of  itself  =  24129  ?  86.  36%  of  itself  =  3360  ? 

83.  10$  of  itself  =  1540  ?  87.  5$  of  itself  =  3078  ? 

84.  33J%  of  itself  =  $3680  ?  88.  25$  of  itself  =  450  ? 

85.  25$  of  itself  =  5000  ?  89.  7-|$  of  itself  =  6475  ? 

90.  Sold  1900  bbl.  flour  for  $11520,  which  was  20$  above 
cost ;  what  was  the  whole  cost  and  the  cost  per  barrel? 


Percentage.  87 

91.  A  dealer  sold  1600  bbl.  beef  for  $24000,  which  was  a 
loss  of  25$ ;  what  did  the  whole  cost,  and  what  did  he  get  a 
barrel  ? 

92.  A  builder  sold  a  house  for  18250,  which  was  12$  more 
than  it  cost  him  ;  what  was  the  cost? 

Exam  ples. 

1.  What  is  the  cost  of  a  house  which  sells  at  a  loss  of  7£$, 
the  selling  price  being  $11500  ? 

2.  A  merchant  owes  $12575,  and  his  assets  are  $7500  ;  what 
per  cent  can  he  pay  ? 

3.  Sold  2  city  lots  at  $1500  each  ;  on  one  I  made  15$,  on 
the  other  I  lost  15$ ;  what  did  I  gain  or  lose  ? 

4.  If  15$  of  what  is  received  for  goods  is  gain,  what  is  the 
gain  per  cent  ? 

5.  Sold  goods  for  $29900  and  made  15$  after  deducting  5$ 
for  cash  ;  what  was  the  cost? 

6.  240  is  33^$  more  than  what  number  ? 

7.  A  collector  who  has  8$  commission,  pays  $534.75  for  a 
bill  of  $775  ;  what  amount  of  the  bill  does  he  collect  ? 

8.  What  is  \%  of  $1728? 

9.  What  is  9|$  of  275  miles? 

10.  What  is  the  difference  between  5£$  of  $800  and  6£$ 
of  $1050  ? 

11.  Bought  300  long  tons  coal  at  $3.75  a  ton  and  sold  it  at 
$4.60  a  short  ton ;  what  is  the  per  cent  profit  ? 

12.  Bought  a  barrel  of  syrup  for  $20 ;  what  must  I  charge  a 
gallon  in  order  to  gain  20$  on  the  whole  ? 

13.  Sold  25  tons  coal  at  $5.64  per  ton,  and  made  $62;  what 
did  the  coal  cost,  and  what  per  cent  was  the  profit  ? 

14.  A  quarter  section  of  land  was  sold  for  $4563,  which  was 
8$  less  than  cost,;  what  was  the  cost  per  acre  ? 

15.  What  $  of  a  number  is  25$  of  3  fourths  of  it? 

16.  \%  of  1258  is  \%  of  what  number? 

17.  What  %  of  a  number  is  20$  of  f  of  it  ? 


88  Percentage. 


APPLICATIONS    OF    PERCENTAGE.* 


PROFIT    AND     LOSS. 

219.  Profit  and  Loss  are  gain  or  loss  in  business  transac- 
tions.    They  are  calculated  by  percentage. 

The  cost  is  the  base  ;  the  per  cent  of  gain  or  loss,  the  rate  ; 
the  gain  or  loss,  the  percentage  ;  the  selling  price,  the  cost, 
plus  or  minus  the  gain  or  loss. 

1.  A  man  paid  $650  for  a  carriage,  and  sold  it  for  8%  more 
than  it  cost  him  ;  what  was  his  profit  ? 

Analysis.— 8%  =  .08,  and  $650  x  .08  =  $52.00,  Arts. 

2.  A  musician  bought  a  piano  for  $570,  and  sold  it  for 
$624.15  ;  what  per  cent  was  his  profit  ? 

Analysis.  —  $624.15  -  $570  =  $5415  (gain),  and  $54.15  -f-  570  =  .095, 
or9|%,  Ans. 

3.  A  provision  dealer  made  $500  on  a  cargo  of  flour,  which 
was  20$  of  the  cost ;  what  was  the  cost  ? 

Analysis.— Since  $500  are  20%  of  a  number,  1%  of  that  number  is 
*V  of  $500  =  $25,  and  100%  is  $25  x  100  =  $2500,  Ans. 
Or,  since  $500  =  £  (20%),  f  =  $500  x  5  =  $2500,  Ans. 

4.  A  merchant  tailor  sold  a  quantity  of  goods  for  $750,  on 
which  he  made  25$  ;  what  did  the  goods  cost  him  ? 

Analysis.— $750  is  the  cost  +25%  of  itself;  and  $750  -f- 1.25  =  $600 
the  cost,  Ans. 

5.  A  grocer  sold  a  quantity  of  damaged  goods  for  $400,  which 
was  20$  less  than  cost ;  what  was  the  cost  ? 

Analysis.— $400  is  the  cost  -20%  of  itself,  and  100% -20%  =  .80, 
$400^-. 80  =  $500,  the  cost,  Ans. 

*  The  Applications  of  Percentage  in  business  transactions  are  numerous  and  impor- 
tant. Special  pains  should  therefore  be  taken  to  have  the  subject  thoroughly  under- 
stood. 


Trade  Discount.  89 

Or,    |  -  \  (20  f0)  =  %  ;     since    §  =  $400,    \  =  $100,    and    |  =  $500. 
(Art.  215,  N.  2.)    Hence,  the 

"  Profit  or  Loss  =  Cost  x  Bate. 
Bate  =  Profit  or  Loss  -^  Cost. 
Formulas.—  {  Cost  =  Gain  or  Loss  -j-  Bate. 

j  Selling  Price  -f-  (1  -f  Bate),  or 
"  [  Selling  Price  -r-  (1  —  Bate). 

Note.— It  often  shortens  the  process  to  take  the  fractional  part  of  the 
base,  indicated  by  the  given  per  cent. 


TRADE     DISCOUNT. 

220.  It  is  customary  for  merchants  and  manufacturers  to 
have  fixed  price  lists  of  their  goods,  and  when  the  market 
varies  instead  of  changing  the  fixed  price  they  change  the  rate 
of  discount.  The  fixed  price  is  named  the  list  price,  and  the 
deduction  made  from  it,  is  called  the  Trade  Discount. 

Note. — Profit  and  Loss  are  calculated  on  the  actual  cost  of  goods,  or 
sum  invested  ;  trade  discount  on  the  list  price. 

221.  Dealers  usually  announce  their  "terms"  upon  their 
"bill  heads"  thus,  Terms  3  months,  or  30  days,  less  5%; 
terms  60  days,  or  %%  discount  in  10  days,  etc. 

Note. — When  bills  are  paid  before  maturity,  merchants  usually 
deduct  the  legal  interest  for  the  time,  on  amount  of  bill. 

222.  To  find  the  Net  Amount  of  Bills  when  discounts  are 
made. 

l.  A  Bill  of  goods  at  list  prices  amounts  to  $105  ;  what  is 
the  net  amount,  the  trade  discount  being  10^,  and  5%  off  for 
cash  ? 

Solution.— $105  x  .10  =  $10.50,  and  $105- $10. 50  s  $94.50.  Again, 
$94.50  x  .05  =  $4,725,  and  $94.50 -$4,725  =  $89,775,  Ans.    Hence,  the 

Eule. — Deduct  the  trade  discount  from  the  list  price, 
and  from  the  remainder  take  the  discount  for  cash. 


90  Percentage. 

Note.  Observe  that  the  first  rate  of  discount  only  is  deducted  from 
the  list  price,  and  the  subsequent  rates  are  deducted  from  the  remainders. 
The  result  is  not  affected  by  the  order  in  which  the  discounts  are  taken. 

2.  What  is  the  net  amount  of  a  bill  of  goods,  the  list  price 
of  which  is  $435,  sold  5$  off  for  cash,  trade  discount  8$? 

3.  Sold  books  on  3  mo.  amounting  to  $854.75  at  a  discount 
of  12$  from  retail  price,  and  10$  off  for  cash ;  what  is  the  net 
value  of  the  bill  ? 

4.  The  gross  amount  of  a  bill  is  $236.37;  the  rates  of 
discount  are  15$  and  8$ ;  what  is  the  net  amount? 

5.  Find  a  direct  discount  equal  to  a  discount  of  12-§-$  and  8%. 

Ans.  19£$. 

Note. — To  find  a  direct  discount  equal  to  two  or  more  taken  in 
succession  ;  from  the  sum  of  two  discounts  subtract  their  product. 

6.  What  direct  discount  is  equal  to  a  discount  of  25$  and 
17$? 

7.  On  a  bill  of  $625,  what  is  the  difference  between  a  discount 
of  30$  and  a  discount  of  25$  and  5$  ? 

8.  Bought  books  at  a  discount  of  20$  on  the  retail  price, 
and  sold  them  at  the  retail  price  ;  what  per  cent  did  I  gain? 

9.  What  per  cent  would  I  gain  at  a  discount  of  33£$  ? 

10.  With  a  trade  discount  of  8$  and  5$  for  cash,  goods 
were  sold  for  $825  at  a  profit  of  15$ ;  what  was  the  cost  ? 

223.  To  Mark  goods  so  that  a  given  per  cent  may  be  deducted 
and  leave  a  given  per  cent  profit. 

11.  Bought  cloaks  at  $75.10;  what  price  must  they  be 
marked,  that  15$  may  be  deducted  and  leaye  25$  profit  ? 

Analysis.— The  selling  price  is  125%  of  $75.10,  and  $75.10x1.25  = 
$93,875.  But  the  marked  price  is  to  be  diminished  by  15%  of  itself,  and 
100%— 15%  =  85%  ;  hence,  $93,875  =  85%  of  the  marked  price.  Now 
$93.875^-. 85  =  $110.44,  the  marked  price.     (Art.  217.)    Hence,  the, 

Rule. — Find  the  selling  price  and  divide  it  by  1  minus 
the  given  per  cent  to  be  deducted ;  the  quotient  will  be 
the  marked  price. 


Commission  and  Brokerage.  91 

12.  A  bookseller  wishes  to  mark  up  the  price  of  a  book 
which  he  now  sells  for  £2,  so  that  he  can  deduct  \§%  and  yet 
receive  the  present  price  ;  what  must  be  the  marked  price? 

13.  A  merchant  sells  cloths  for  $268  by  which  he  gains  23%; 
how  must  he  mark  them  so  that  he  may  deduct  4$  and  make 
the  same  profit? 

14.  Bought  diamonds  at  $920 ;  how  must  I  mark  the  price 
that  after  abating  b%  the  profit  may  be  25%  ? 

15.  What  must  be  the  price  of  an  article  from  which  you 
deduct  20%  and  leave  20  cents  ? 

COMMISSION    AND     BROKERAGE. 

224.  Commission  is  an  alloivance  made  to  agents,  collectors, 
brokers,  etc.,  for  the  transaction  of  business. 

Brokerage  is  Commission  paid  a  broker. 

Guarantee  is  the  %  charged  for  assuming  the  risk  of  loss. 

Notes. — 1.  An  Agent  is  one  who  transacts  business  for  another,  and  is 
often  called  a  Commission  Merchant,  Factor,  or  Correspondent. 

2.  A  Collector  is  one  who  collects  debts,  taxes,  duties,  etc. 

3.  A  Broker  is  one  who  buys  and  sells  gold,  stocks,  bills  of  exchange, 
etc.  Brokers  are  commonly  designated  by  the  department  of  business  in 
which  they  are  engaged  ;  as,  Stock-brokers,  Exchange-brokers,  Note- 
brokers,  Merchandise-brokers,  Real -estate-brokers,  etc. 

225.  Goods  sent  to  an  agent  to  sell,  are  called  a  Consignment ; 
the  person  to  whom  they  are  sent,  the  Consignee;  and  the 
person  sending  them  the  Consignor  or  Shipper. 

226.  The  Gross  Proceeds  of  a  business  transaction  are  the 
whole  sum  received. 

227.  The  Net  Proceeds  are  the  gross  amount  received,  minus 
the  commission  and  other  charges. 

228.  Commission  and  Brokerage  ■  are  computed  by  Per- 
centage ;  the  money  employed  is  the  base  ;  the  per  cent  for 
services,  the  rate  ;  the  commission,  the  percentage. 


92  Percentage. 

Note. — Brokerage  is  computed  on  the  par  value  of  stocks,  bonds,  etc., 
as  the  base. 

1.  Find  Z\%  commission  on  sales  for  $8168.     (Art.  215.) 

Am.  $285.88. 

2.  What  is  the  commission  at  %\%  for  selling  875  bushels  of 
wheat,  at  $1.25  ? 

3.  An  agent  collects  $2850 ;  how  much  does  he  pay  to  the 
owner  after  deducting  b%  commission  ? 

4.  A  commission  merchant  sold  goods  amounting  to 
$2875.50  ;  the  charges  were  %\%  com.,  %\%  guarantee,  cartage, 
storage,  etc.,  $18.50  ;  how  much  was  due  the  owner  ? 

5.  Paid  $375  to  an  auctioneer  for  selling  a  house  ;  his  com. 
being  %\%,  for  how  much  did  he  sell  it  and  what  did  the  owner 
receive?     (Art.  217.) 

6.  An  agent  received  $864  with  which  to  buy  goods ;  he 
was  to  have  2\%  commission  on  the  amount  of  purchase ;  how 
much  was  his  commission  and  what  the  amount  of  purchase  ? 

7.  A  commission  merchant  received  $654;  he  charged  %\% 
commission  and  *Z\%~  for  guarantee ;  what  were  the  net 
proceeds  ? 

8.  An  agent  charged  %%  commission  and  $58.60  expenses 
for  selling  a  house,  and  sent  the  owner  $16350 ;  for  what  did 
he  sell  the  house  ? 

9.  What  is  the  brokerage,  at  \%>  on  the  sale  of  stock,  the 
market  value  of  which  is  $5250  ? 

10.  Paid  a  broker  $25  for  buying  bank  stock  at  par,  com- 
mission \% ;  how  much  did  he  invest  ? 

11.  The  sum  of  $25365  sent  to  my  agent,  includes  invest- 
ment and  commission  at  3f  %  ;  what  is  the  investment  ?  What 
is  the  commission  ? 

12.  My  agent  bought  tea  at  \%  brokerage,  and  was  paid 
$450.  He  afterwards  sold  the  tea  at  a  profit  to  me  of  $6150, 
deducting  1  \%  commission  on  the  sale ;  how  much  was  his 
commission  ? 

13.  A  man  wishes  to  draw  on  New  York  for  an  amount 
sufficient  to  cover  expenses  of  %%  exchange  and  2\%  commis- 
sion, and  leave  him  the  sum  of  $5242.50;  for  how  much  must 
he  draw  ? 


Brokerage.  93 

14.  What  number  diminished  by  ty%  of  itself  is  equal 
to  895  ? 

15.  A  bill  of  $875  was  placed  in  the  hands  of  a  collector, 
who  obtained  75%  of  it  and  charged  8%  commission ;  how 
much  did  the  owner  receive  ? 

16.  A  man  invested  $6350  in  U.  S.  bonds  at  105$,  broker- 
age 1 1%,  and  sold  them  at  115%,  brokerage  If  %  \  how  much  did 
he  gain  ? 

17.  On  what  valuation  is  $18.25  the  commission,  at  \%  ? 

18.  On  what  sales  is  $825.50  the  commission,  at  7%%? 

19.  A  merchant  sold  on  a  commission  of  8^%,  200  bbl.  pork, 
each  weighing  200  lb.,  at  12J  cts.  a  pound  ;  what  was  the 
amount  of  his  commission,  and  how  much  did  he  remit  to  the 
owner  ? 

20.  A  lawyer  received  $6.80,  being  8%  commission  for  col- 
lecting a  note  ;  what  was  the  face  of  the  note  ? 

21.  A  real-estate  agent  bought  land  for  which  he  received 
2|%  commission  for  buying  and  $48.50  for  charges.  The  whole 
cost  of  land,  commission,  and  charges  was  $8450 ;  what  was 
paid  for  the  land  ? 

22.  A  commission  merchant  sells  60  bbl.  potatoes  at  $3.25  a 
bbl.,  and  42  bu.  beans  at  $2.50  a  bu. ;  how  much  is  due  the 
consignor,  the  commission  being  2f%  ? 

23.  An  agent  who  charged  2J$  for  selling  a  house,  paid  the 
owmer  $12360  ;  what  did  he  get  for  the  property? 

24.  On  what  amount  of  sales  is  $241.75  the  commission,  at 
15%,  after  deducting  $18.20  for  expenses? 

25.  An  agent  received  $67.50  for  collecting  $4500  ;  what  was 
the  rate  ? 

26.  A  man  sends  $3246.20  to  an  agent  in  Boston  to  buy 
shoes,  deducting  his  commission  at  2% ;  what  was  his  com- 
mission ?     How  much  did  he  spend  for  shoes  ? 

27.  A  New  York  firm  sell  for  me  goods  at  6%  commission  ; 
how  mucli  must  be  sold  that  my  broker  can  buy  stock  with 
the  proceeds  to  the  value  of  $6250,  after  deducting  his  com- 
mission of  %\%t 

28.  A  dealer  in  pork  cleared  $1565,  charging  10%'  commis- 
sion ami  paying  $850  expenses  of  packing  ;  if  the  pork  cost 
him  7  cts.  a  pound,  how  many  pounds  did  he  pack  ? 


94  Percentage. 


INSURANCE. 

229.  Insurance  is  security  against  loss.  It  is  distinguished 
by  different  names,  according  to  the  cause  of  the  loss  or  the 
object  insured.  Thus,  Fire  Insurance,  Marine  Insurance, 
Accident,  Health,  Life  Insurance,  etc.   (See  Life  Ins.,  Art,  566.) 

Note. — Risks  of  transportation  partly  by  land  and  partly  by  water,  are 
called  Transit  Insurance. 

230.  The  parties  who  agree  to  make  good  the  loss,  are 
called  Insurance  Companies  or  Underwriters. 

Note. — When  only  a  part  of  the  property  insured  is  destroyed,  the 
underwriters  are  required  to  make  good  only  the  estimated  loss. 

231.  Insurance  Companies  are  of  two  kinds:  Stock  Com- 
panies and  Mutual  Companies. 

232.  A  Stock  Company  is  one  which  has  a  paid-up  capital, 
and  divides  the  profit  and  loss  among  its  stockholders. 

233.  A  Mutual  Company  is  one  in  which  the  losses  are 
shared  by  the  parties  insured. 

Note. — Some  companies  combine  the  principles  of  Stock  and  Mutual 
Companies,  and  are  called  Mixed  Companies. 

234.  The  Premium  is  the  sum  paid  for  insurance. 

235.  The  Policy  is  the  written  contract  between  the  insurers 
and  the  insured.     They  usually  run  from  one  to  five  years. 

236.  A  Valued  or  Closed  Policy  contains  a  certain  fixed 
value  on  the  thing  insured ;  as  of  houses,  goods,  etc. 

237.  An  Open  Policy  is  one  in  which  the  value  of  the  article 
insured  is  to  be  determined  in  case  of  loss. 

238.  The  rate  of  premium  charged  depends  on  the  nature 
of  the  risk  and  the  time  for  which  the  policy  is  issued,  the  rate 
for  long  policies  being  less  than  for  short  ones. 


Insurance.  95 

239.  Rates  for  less  than  a  year  are  called  Short  Rates. 

Notes. — 1.  Policies  are  renewed  annually,  or  at  stated  periods,  and  the 
premium  is  paid  in  advance.  In  this  respect  insurance  differs  from  com- 
mission, etc.,  which  have  no  reference  to  time. 

2.  When  a  policy  taken  for  a  year  is  cancelled  prior  to  the  end  of  the 
year,  a  Return  Premium  is  paid  to  the  party  insured. 

240.  Premiums  are  computed  by  the  rules  of  Percentage. 
Rates  of  premium  are  a  per  cent  of  the  sum  insured,  or  a  num- 
ber of  cents  paid  on  $100. 

Thus,  25  cts.  on  $100,  is  \  of  1  %  ;  75  cts.  on  $100  is  f  % . 

241.  An  Insurance  Agent  is  a  person  who  acts  for  Insur- 
ance Companies  iu  obtaining  business,  collecting  premiums, 
adjusting  losses,  etc. 

242.  An  Insurance  Broker  is  a  person  who  negotiates  insur- 
ance and  receives  a  percentage  from  the  company  taking  the 
risk. 

Note. — Insurance  Brokers  are  regarded  as  agents  of  the  insured. 

243.  The  Surplus  of  an  Insurance  Company  is  the  excess  of 
its  assets  above  its  liabilities. 

244.  To  find  the  Premium,  from  the  sum  insured  and  the  rate. 

1.  What  is  the  premium  for  insuring  a  store  and  goods 
valued  at  $12000,  at  \\%  for  1  year  ? 

Solution.— $12000  x  .015  =  $180.00,  Am.    Hence,  the 
Formula.—  Pr em i um  =  Sum  In.  x  Rate.     (Art.  215.) 

2.  What  is  the  cost  of  insuring  goods  worth  $4000,  at 
80  cents  per  $100,  the  policy  and  survey  being  $1.50  ? 

3.  If  I  take  a  risk  of  $12000  at  a  premium  of  1|£,  and  re-\ 
insure  it  at  \\%,  what  will  be  my  gain  ? 

4.  Insured  a  cargo  from  Liverpool  worth  £850  10s.  4d.,  at  a 
premium  of  \\%\  at  $4.86  to  the  £,  what  is  the  premium  in 
U.  S.  Money? 


96  Percentage. 

245.  To  find  the  Rate,  from  the  sum  insured  and  the  premiumc 

5.  A  man  paid  $215  for  insuring  $8600  on  a  tenement  house; 
what  was  the  rate  ? 

Solution.—  $215. 00  h- $8600  =  .025,  or  2*-%,  Ans.     Hence,  the 

Formula. — Rate  =  Premium-?- Ami.  Insured.    (Art.  216.) 

6.  A  grocer  paid  $40  annually  for  an  insurance  of  $5000  on 
his  goods  ;  what  was  the  rate? 

7.  If  the  owner  pays  $2800  for  insuring  a  steamer  worth 
$42000,  what  rate  per  cent  does  he  pay  ? 

8.  Paid  $25  for  an  insurance  of  $3000  ;  what  was  the  rate  ? 

246.  To  find  the  Sum  Insured,  when  the  premium  and  the 
rate  per  cent  are  given. 

9.  A  merchant  paid  $1200  premium,  at  2\%,  on  a  ship  and 
cargo  from  Liverpool  to  Baltimore  ;  it  was  lost  on  the  voyage  ; 
what  amount  of  insurance  should  he  recover  ? 

Solution.— $1200.000-*-. 022  =  $54545.455,  Ans.    Hence,  the 
Formula. — Sum  Insured  =  Premium-?- Rate.     (Art.  217.) 

10.  If  I  pay  $254  premium  on  silks,  from  Havre  to  New 
York,  at  1\  per  cent,  what  amount  does  my  policy  cover  ? 

11.  A  gentleman  paid  $62  annually  for  insuring  house  and 
furniture,  which  was  2\%  on  half  its  value;  what  was  its  value  ? 

12.  How  much  insurance  can  be  obtained  for  $125  on  a  store 
and  contents,  at  1-|%  ? 

13.  Paid  $287  to  insure  half  the  value  of  a  cargo  at  2f  %  5 
what  was  its  total  value  ? 

247.  To  find  the  sum  to  be  insured  to  cover  the  value  of  the 
goods  and  premium. 

14.  Goods  bought  in  Paris  for  $7594,  were  insured  at  2\% ; 
what  sum  will  cover  the  value  of  the  goods  and  the  premium  ? 

Anatasis. — The  sum  insured  is  100%  of  itself,  the  premium  is  21' <  of 
that  sum,  and  100% -24%  =  97|%.  Now  $7594-:-. 97i  =  $7788.72,  the 
sum  required.     (Art.  J518.)    Hence,  the 

Formula. — Sum  Insured  ==  Value  -f*  (1  -—  Rate), 


Insurance,  97 

15.  If  a  warehouse  is  worth  $266250,  what  sum  must  be 
Insured,  at  %%,  to  cover  the  property  and  premium  ? 

16.  What  sum  must  be  insured,  at  3%,  on  a  consignment  of 
tea  worth  $4200,  to  cover  property  and  premium  ? 

17.  A  merchant  sent  a  cargo  of  goods  worth  $25275  to 
Canton ;  what  sum  must  he  get  insured  at  3%,  that  he  may 
suffer  no  loss,  if  the  ship  is  wrecked  ? 

18.  The  premiums  paid  for  insuring  two  stores,  are  $98.25 
and  $146.50  ;  the  rate  is  lf%  ;  what  sum  must  be  insured  to 
cover  the  property  and  premium  ? 

Examples. 

1.  What  is  the  annual  premium  on  a  policy  insuring  a  house 
for  -jj-  its  value,  at  \%  ? 

2.  If  $125  are  paid  annually  for  insuring  $24000,  what  is  the 
rate  per  cent  ? 

3.  What  premium  must  be  paid  for  insuring  $6500  on  a 
store  for  3  years  at  %\%  ? 

4.  A  house  is  insured  at  f%,  and  the  premium  is  $93.60; 
for  how  much  is  it  insured  ? 

5.  A  shipowner  insures  a  ship  and  cargo  for  $89325,  at  4-|%, 
the  policy  covering  both  property  and  premium ;  what  is  the 
value  of  the  property  ? 

6.  What  will  it  cost  to  insure  a  factory  worth  $26000  at  \%, 
and  machinery  worth  $16800  at  \%,  with  $1.50  for  policy? 

7.  Paid  $350  on  a  shipment  of  goods  to  insure  \  the  value, 
at  2>\% ;  what  was  the  whole  value  ? 

8.  A  company  had  $125  premium  for  insuring  property  worth 
$18000 ;  if  similar  property  worth  $45000  were  insured  at  the 
same  rate  in  another  company,  what  would  be  the  premium  ? 

9.  A  dealer  insured  a  stock  of  goods  for  1  year,  at  \\%\  if 
the  short  rate  for  6  mo.  was  83  cents  on  $100,  and  the  policy 
was  cancelled  at  the  end  of  that  time,  what  should  be  the 
return  premium,  the  goods  being  insured  for  $3500  ? 

Note. — Multiply  the  sum  insured  by  the  difference  between  the  given 
rates. 

7 


98  Percentage. 

ADJUSTMENT     OF     LOSSES. 

248.  Losses  may  be  partial  or  total. 

In  ordinary  cases  of  partial  loss,  the  insured  is  entitled  to 
indemnity  only  for  the  actual  loss.  If  a  total  loss  occurs,  the 
insurers  pay  the  full  amount  of  their  policy. 

249.  If  the  policy  contains  the  "Average  Clause,"  the  com- 
pany pays  only  such  a  proportion  of  the  loss  as  the  amount 
insured  is  to  the  value  of  the  property  insured. 

Thus,  a  person  who  has  a  policy  with  the  "  Average  Clause  "  for  $1000 
on  property  worth  $2000,  would  receive 


Note. — It  is  customary  for  Insurance  Companies  to  reserve  the  right 
to  repair  or  replace  the  damaged  property. 

250.  If  the  loss  is  partial,  but  amounts  to  more  than  half 
the  value  of  the  property,  the  owner  has  the  right  to  transfer 
to  the  company  what  remains,  and  claim  the  full  value  of  the 
property.*  This  is  called  the  right  of  abandonment,  and  the 
company  cannot  refuse  to  take  it,  unless  specially  named  in 
the  policy. 

251.  When  a  partial  loss  occurs  to  a  vessel,  the  companies 
pay  such  proportion  of  it  as  the  sum  insured  is  to  the  value  of 
the  property.  It  is  an  established  rule  that  one-third  shall  be 
allowed  the  insurers  for  the  superior  value  of  the  new  material 
used  ;  that  is,  "  one-third  off,  new  for  old." 

252.  A  total  loss  may  be  actual  or  constructive. 

An  Actual  Total  Loss  is  one  by  which  the  property  insured 
is  entirely  destroyed  by  fire  or  water.     (Art.  230,  N.) 

A  Constructive  Total  Loss  is  one  in  which  some  portions  of 
the  property  are  saved,  and  are  transferred  by  the  insured  to 
the  insurers  by  abandonment. 

*  American  Cyclopedia, 


Adjustment  of  Losses.  99 

253.  In  such  cases  the  insurers  pay  for  the  whole,  and  hold 
the  salvage  or  property  saved  as  their  own. 

254.  To  estimate  proportionate  losses. 

1.  A  merchant  insured  $2500  in  a  Mutual  Co.,  $1500  in 
the  Howard,  and  $3500  in  the  Phoenix;  a  loss  by  fire  of  $6000 
occurred  ;  how  much  should  each  company  pay  ? 

Explanation. — The  total  sum  insured  was  $2500  M. 

$7500,  the  loss  was  $6000.     Dividing  $6000  by  -^qq  jj 

$7500  gives  80  % ,  proportion  of  insurance  to  loss.  3500  P 

Share  of   Mutual  a   $2500  x  .80  =  $2000.00,  _oOW  r. 

of     the     Howard  =  $1500  x  .80  =  $1200.00,  $7500  Sum  Ins. 

of     the     Phoenix  -  $3500  x  .80  =  $2800.00.  6000-^7500  =  .80. 
Hence,  the 

Kule. — Divide  the  loss  by  the  total  insurance,  the  quo- 
tient will  be  the  per  cent  which  each  must  pay. 

2.  The  loss  by  fire  on  a  piece  of  property  was  $8000,  of  which 
$2000  was  insured  in  the  Howard,  $3000  in  the  Phoenix,  and 
$3000  in  the  Manhattan  Company ;  how  much  did  each  com- 
pany contribute  ? 

3.  The  loss  by  fire  on  a  store  and  contents  was  $4525  ;  the 
property  was  insured  $2500  in  Franklin  Company,  $4000  in 
Mutual,  $2000  in  Phoenix,  and  $3000  in  Hanover  Company  ; 
how  much  should  each  pay  ? 

4.  A  shipment  of  silks  valued  at  $25000  was  insured  for 
$15000,  with  a  policy  containing  the  "  average  clause  ;"  if  the 
goods  were  damaged  to  the  amount  of  $5000,  how  much  would 
be  paid  by  the  company  ? 

5.  A  cargo  of  oil  worth  $30000  was  insured  for  18  months  at 
%\% ;  at  the  end  of  12  months  the  policy  was  cancelled  ;  if  the 
short  rate  for  6  months  was  65  cts.,  what  should  be  the  return 
premium  ? 

6.  A  real-estate  owner  insured  $75000  at  the  average  rate  of 
\%  a  year  for  12  years  ;  the  entire  property  being  at  the  end  of 
10  years  destroyed  by  fire,  the  company  paid  the  loss  in  full; 
how  much  was  the  real  loss  to  the  company,  the  insurance 
having  been  regularly  paid  ? 


100  Percentage. 


TAXES. 

255.  A  Tax  is  a  sum  assessed  upon  the  person,  property,  or 
income  of  citizens. 

256.  A  Property  Tax  is  a  tax  upon  property. 

257.  A  Personal  Tax  is  a  tax  upon  the  person,  and  is  called 
a  poll  or  capitation  tax. 

Notes. — 1.  A  Poll  Tax  is  a  specific  sum  levied  in  some  States  upon  all 
male  citizens  not  exempt  by  law,  without  regard  to  property. 

2.  In  Mass.  a  poll  tax  is  assessed  on  every  male  inhabitant  above  the 
age  of  20  years,  whether  a  citizen  of  the  U.  S.  or  an  alien.     Rev.  Stat. 

258.  A  License  Tax  is  the  sum  paid  for  permission  to  pur- 
sue certain  avocations. 

259.  Special  Taxes  are  fixed  sums  assessed  upon  certain 
articles  of  luxury  ;  as  carriages,  billiard  tables,  gold  watches,  etc. 

Note  — The  Internal  Revenue  or  Stamp  Tax  upon  perfumery,  watches, 
proprietary  medicines,  etc.,  was  repealed  by  Act  of  Congress  in  Oct.  1882. 

260.  Property  is  of  two  kinds,  real  and  personal. 

261.  Real  Estate  is  that  which  is  fixed ;  as,  houses  and 
lands. 

262.  Personal  Property  is  that  which  is  movable;  as,  money, 
stocks,  bonds,  mortgages,  etc. 

263.  Assessors  are  persons  appointed  to  make  a  list  of 
taxable  property  and  fix  its  valuation  for  the  purpose  of 
taxation. 

264.  A  Collector  is  a  person  appointed  to  receive  the  taxes. 

265.  Property  taxes  are  computed  by  Percentage. 

266.  An  Assessment  Roll  is  a  list  of  all  persons  in  the  dis- 
trict liable  to  be  assessed,  with  their  taxable  property  and  its 
valuation. 


Taxes.  101 

267.  To  Assess  a  Property  Tax,  when  the  sum  to  be  raised  and 
the  valuation  of  the  property  are  given. 

1.  In  a  city  whose  property  was  valued  at  $2500000,  a  tax  of 
$15000  was  levied ;  there  being  250  polls,  each  taxed  $2,  what 
was  the  rate  of  the  tax,  and  what  A's  tax  whose  real  estate  was 
valued  at  $8000,  and  personal  at  $5000  ? 

Explanation. — The  sum  to  be  raised  is  $15000  solution. 

less  $500  on  the  polls,  equal  to  $14500  on  the      Town  tax  $15000 
property;  and  $14500 -*- $2500000  =  $.0058.  or  5.8      p0H       «  500 

mills  on  a  dollar.  OKnnnnn  \  <i»i  akcci 

A's  property  is  $8000  +  $5000  =  $13000.    As  he      ^500000  )  $14o00 

pays  .0058  on  $1,  on  $13000  he  pays  $13000  x  .0058.      Kate  .0058 

=  $75.40  +  $2  (poll  tax)  =  $77.40. 

Ans.  The  rate  is  .0058  and  his  tax  $77.40.     Hence,  the 

Rule. — I.  From  the  sum  to  be  raised  subtract  the  poll 
tax  and  divide  the  remainder  by  the  amount  of  taxable 
-property ;  the  quotient  will  be  the  rate. 

III.  Multiply  the  valuation  of  each  man's  property  by 
the  rate,  and  the  product  plus  his  poll  tax  will  be  his 
entire  tax. 

Note. — The  commission  for  collecting  taxes  is  commonly  included  in 
the  net  sum  to  be  raised. 

2.  A  tax  of  $25250  was  levied  upon  a  township.  The  valua- 
tion of  its  real  estate  was  $1000000,  the  personal  $400000,  and 
it  had  500  taxable  polls  assessed  at  $1.50  each.  What  was  the 
rate  of  taxation,  and  what  was  A's  tax  whose  real  estate  was 
valued  at  $6000,  personal  property  at  $4000,  and  who  paid  for 
two  polls  ? 

Analysis. — Sum  assessed  on  the  polls  =  $1.50  x  500  =  $750,  and 
$25250— $750  =  $24500,  sum  assessed  on  property.  Amount  of  taxable 
property  =  $1400000,  and  $24500 -*-$  1400000  =  $.0175,  or  If  %. 

A's  taxable  property  is  $6000  +  $4000  =  $10000. 

By  the  table  the  tax  on  $10000  =  $175. 

Tax  on  polls  =  $3,  and  $175  +  $3  =  $178,  Ans. 

3.  For  the  purpose  of  grading  a  street,  the  property  in  a 
certain  locality  was  assessed  at  the  rate  of  6  mills  on  the  dollar ; 
what  was  a  man's  tax  whose  property  was  valued  at  $8500  ? 


102 


Percentage. 


Tax    Table. 

Showing  the  tax  on  sums  from  $1  to  $10000,  at  \\%. 


Pbop. 

Tax. 

Pbop. 

Tax. 

Pbop. 

Tax. 

_ — .., 

Prop.    Tax. 

$1 

10175 

$10 

$.175 

$100 

$1.75 

$1000  $17.50 

2 

.035 

20 

.35 

200 

3.50 

2000  35.00 

3 

.0525 

30 

.525 

300 

5.25 

3000  52.50 

4 

.07 

40 

.70 

400 

7.00 

4000  70.00 

5 

.0875 

50 

.875 

500 

8.75 

5000  87.50 

6 

.105 

60 

1.05 

600 

10.50 

6000  105.00 

7 

.1225 

70 

1.225 

700 

12.25 

7000  122.50 

8 

.14 

80 

1.40 

800 

14.00 

8000  140.00 

9 

.1575 

90 

1.575 

900 

15.75 

9000  157.50 

10 

.175 

100 

1.75 

1000 

17.50 

10000  175.00 

4.  What  was  B's  tax  whose  real  estate  was  valued  at  $8000, 
personal  $5000,  and  who  paid  for  3  polls  ? 

5.  What  is  B's  tax,  the  valuation  of  whose  property  is  $4240, 
and  is  assessed  for  2  polls,  at  $1.50  ? 

6.  What  is  C's  tax,  who  is  assessed  for  1  poll  and  whose 
property  is  estimated  at  $31250  ? 

7.  D  is  assessed  for  $17225  and  1  poll ;  what  is  his  tax? 

8.  B  is  assessed  for  $28265  and  1  poll ;  what  is  his  tax  ? 

268.  To  find  the  Amount  to  be  assessed,  when  the  Net  Sum 
and  the  Rate  for  Collecting  are  given. 

9.  A  union  school  district  required  $48355  to  build  a  school- 
house;  what  amount  must  be  assessed  in  order  to  pay  the 
expense  and  the  commission  of  5%  for  collecting  ? 

Solution.— $48355-*- .95(1-. 05)  =  $50900,  Ans.    (Art.  218.) 

Eule. — Divide  the  net  sum  by  1  minus  the  rate ;  the 
quotient  will  be  the  amount  to  be  assessed.     (Art.  218.) 
Note. — The  valuation  =  Amt.  to  be  raised  -=-  rate. 

10.  What  sum  must  be  assessed  to  raise  $12600  net,  and 
pay  the  commission  at  4|$  for  collecting  ? 


HTEEEST 


(9-*- 


269.  Interest  is  the  money  paid  for  the  use  of  money. 

270.  The   Principal  is  the   money  for  the   use  of  which 
interest  is  paid. 

271.  The  Rate  is  the  per  cent  of  the  principal,  paid  for  its 
use  1  year,  or  a  specified  time. 

272.  The  Amount  is  the  sum  of  the  principal  and  interest. 

273.  Simple  Interest  is  the  interest  on  the  principal  only. 

274.  Legal  Interest  is  the  rate  established  by  law. 

275.  Usury  is  a  higher  than  the  legal  rate. 


Table. 

276.  Legal  rates  of  interest  in  the  several  States  and  Territories,  com- 
piled from  the  latest  official  sources.  The  first  column  shows  the  legal 
rate  of  interest  when  no  rate  is  specified  ;  the  second  the  maximum  rate 
allowed  by  law. 


States. 

Rate%. 

States. 

Rate  %. 

States. 

Rate  %. 

States. 

Rate%. 

Ala 

Ark.... 
Arizona 

Cal 

Conn. . . 
Colo.... 
Dakota. 

Del 

Flor. . . . 

Ga 

Idaho... 
Ul 

8 
6 

10 

10 
6 

10 
7 
6 
8 
7 

10 
6 

8 

10 

Any* 

Any. 

6 
Any. 

12 

6 

Any. 
8 
18 
8 

Ind.  Ter 
Ind.  .. 
Iowa . . . 
Kan. . . . 

Ky 

La 

Maine . . 
Md..  .. 
Mass..  . 
Mich... 
Minn . . . 
Miss — 

6 
6 
6 

7 
6 
5 
6 

G 
6 

7 
7 
6 

Any. 
8 
10 
12 
6 
8 
Any. 

6 

Any. 

10 

10 

10 

Mo 

Montana 
N.  H. . . . 

N.  J 

N.  Mex.. 
N.  Y.... 

N.  a... 

Neb 

Nevada- 
Ohio.... 
Oregon  . 
Penn. . . . 

6 
10 

6 
6 
6 
6 
6 
7 

10 
6 

10 
6 

10 

Any. 

6 

6 
Any. 

6 

8 

10 

Any. 

8 
12 

6 

R.I 

S.C 

Tenn . . . 
Texas  . . 
Utah. . . . 

Vt 

Va 

W.  Va.. 
W.T.... 

Wis 

Wy 

D.C.... 

6 

7 
6 
8 

10 
6 
6 
6 

10 
7 

12 
6 

Any. 
7 
6 
12 
Any. 
6 
6 
8 
Any. 

10 

Any. 

10 

*  By  special  agreement. 


104  Percentage. 

211.  Interest  is  an  application  of  Percentage;  the  only  dif- 
ference is  that  the  element  of  time  is  connected  with  the  rate 
per  cent. 

Note. — In  computing  interest,  a  legal  year  is  12  calendar  months. 

278.  The  Principal  is  the  Base;  the  per  cent  per  annum,  or 
a  specified  time,  is  the  Rate;  the  Interest  is  the  Percentage; 
the  Sum  of  the  principal  and  interest,  the  Amount. 

General     Method. 

279.  To  compute  interest  for  any  given  time  and  rate. 

l.  What  is  the  interest  of  $450  for  3  yr.  2  mo.  12  d.  at  1%  ? 

Explanation. — First  find  the  time  by  fractions. 

in  years  and  fractions  of  a  year.     Re-  12  d.  =  •£■§-,  or  |  mo. 

ducing  the  days  to  the  fraction  of  a  2-1  mo.-^-12  =  4-|  01*  -^j-  yr. 
month,  if  =  f  mo.,  then  2|  mo.  reduced  3  yr#  2  mo.  12  d.  =  3.2  yr. 
to  the  fraction  of  a  year  =  £§ ,  or  -^  yr. 

Therefore,  the  time  is  3.2  years.  BT  decimals. 

30      12  d. 

Or,  finding  the  decimal  of  a  year  as  in  the  margin,  -j^  24  mo. 
the  time  is  3.2  yr.,  as  before.     (Art.  154.) 


3.2  yr. 

Multiplying  the  principal  $450  by  .07  =  $31.50    int.  1  yr. 
The  interest  for  1  yr.  multiplied  by  3.2       Time  in  years, 

the  number  of  years  and  decimals  of    $100.80,  Ans. 
a  year  gives  the  interest  required.     Hence,  the 

General     Rule. 

Multiply  the  principal  by  the  rate ;  the  result  will  be 
the  interest  for  1  year. 

Multiply  the  interest  for  one  year  by  the  time  in  years 
and  fractions  of  a  year ;  the  product  will  be  the  interest 
required. 

To  find  the  amount,  add  the  interest  to  the  principal. 

Notes. — 1.  When  a  fraction  occurs  after  finding  two  decimal  figures, 
it  may  be  annexed  to  these  figures  as  a  part  of  the  multiplier. 

2.  When  the  rate  per  month-  is  given,  multiply  the  principal  by  the 
rate  per  month,  and  that  product  by  the  number  of  months. 


Interest.  105 

280.  The  work  may  sometimes  be  shortened  by  multiplying 
the  principal  by  the  product  of  the  rate  and  time,  instead  of  by 
these  factors  separately.     (Ex.  2.) 

2.  What  is  the  interest  of  $530  for  2  yr.  3  mo.  at  4%  ? 

Solution.— $530  x  4  =  $21.20,  and  $21.20  x  8}  (time)  =  $47.70. 
Or,  multiplying  the  principal  by  .09  (.04  x  2|)  =  $47.70,  Ans. 

3.  What  is  the  interest  of  $684.85  for  2  yr.  6  mo.  18  d., 
at  5%? 

4.  Find  the  interest  of  $3265.50  for  3  yr.  1  mo.,  at  8%. 

5.  Find  the  interest  of  $2866  for  5  yr.  3  mo.,  at  Q%. 

6.  Find  the  interest  of  $3568  for  4  yr.  2  mo.,  at  ty%. 

7.  Find  the  interest  of  $5465.60  for  3  yr.  4  mo.,  at  §\%. 

8.  What  is  the  interest  on  a  note  of  $165,  dated  Jan.  4,  1880, 
to  Apr.  22d,  1882,  at  6  per  cent  ? 

Note.— From  Jan.  4,  1880,  to  Jan.  4,  1882  =  2  yr. 

From  Jan.  4th  to  Apr.  4th  =  3  mo. 

From  Apr.  4th  to  Apr.  22d  = 18  d. 

Time  —  2  yr.  3  mo.  18  d.,or2.3yr. 

9.  Wrhat  is  the  interest  of  $270  from  June  19, 1880,  to  July 
1,  1881,  at  1%  ? 

10.  What  is  the  interest  of  $205.63  from  Jan.  22,  1879,  to 
Aug.  25,  1880,  at  5%? 

11.  Find  the  interest  and  amount  of  $2500  for  1  yr.  3  mo. 
12  d.,  at.  4±%. 

281.  Method  by  Aliquot  Parts.    (Arts.  192,  206.) 

12.  What  is  the  interest  of  $870  for  3  yr.  4  mo.  15  d.,  at  1%  ? 


Explanation. — The  given  principal  is 
This  multiplied  by  the  rate  .07  =  $60.90     int.  1  yr. 

For  3  years  the  int.  is  3  times  the  int.  for  1  yr.  3 

4  mo.  =  \  yr.,  and  15  d.  —  }  mo.,  and  $182.70    Int.  3  yr. 

$60.90  (int  1  yr.)-=-3  =  int.  for  4  mo.  {\  oft  yr.)  =    20.30    int.  4  mo. 
i  of  *20.30  =  $5,075  (int.  1  mo.),  $5,075-^2         =      2.5375    int.  15  d. 
Total  interest  for  3  yr.  4  mo.  15  d.  =  $205.5375,  Ans. 


106  Percentage. 

Rule. — For    1    Year. — Multiply  the  principal  by  the 
rate. 

For  2  or  more  Years. — Multiply  the  interest  for  1  year 
by  the  number  of  years. 

For  Months. — Take  the  aliquot  part  of  1  year's  interest. 

For  Days. —  Take  the  aliquot  part  of  1  month's  interest. 

Notes. — 1.  For  1   month  take  ^  of  the  interest  for   1   year ;    for 

2  months,  £  ;  for  3  months,  |,  etc. 

2.  For  1  day  take  fo  of  the  interest  for  1  month ;  for  2  days,  ^  ;  for 

3  days,  fo  ;  for  6  days,  ^  ;  for  10  days,  ^,  etc. 

3.  In  computing  interest  30  days  are  commonly  considered  a  month. 

13.  What  is  the  interest  of  $1684  for  1  yr.  9  mo.  10  d.,  at  6%  ? 

14.  Find  the  interest  at  6%  of  $2340  for  1  mo.  15  days. 

15.  Find  the  interest  at  Q%  of  $8700  for  1  yr.  2  mo.  12  d. 

16.  Find  the  amount  of  $4470  for  10  d.  at  4$. 

17.  What  is  the  interest  of  $1234  from  Apr.  10,  1874,  to 
Oct.  1,  1875,  at  6%  ? 

18.  What  was  the  amount  of  $1895.23  from  June  25,  1878, 
to  March  31,  1880,  at  6%? 


Find  the  interest  at  6%  on  Find  the  amount  at  7%  on 

19.  $850,  1  yr.  3  mo.  15  d.  25.  $1864,  2  yr.  8  mo.  5  d. 

20.  $689,  2  yr.  6  mo.  10  d.  26.  $6500,  3  yr.  2  mo.  3  d. 

21.  $738,  2  yr.  4  mo.  12  d.  27.  $1156,  11  mo.  20  d. 

22.  $358,  2  yr.  9  mo.  18  d.  28.  $894,  1  yr.  6  mo.  3  d. 

23.  $755,  3  yr.  7  mo.  9  d.  29.   $765,  2  yr.  4  mo.  20  d. 

24.  $468,  4  yr.  3  mo.  3  d.  30.   $865,  3  yr.  2  mo.  15  d. 

31.  A  note  for  $560.60,  dated  May  5,  1881,  was  paid  Dec.  31, 
1882,  with  interest  at  1%  ',  what  was  the  amount  ? 

32.  If  I  have  the  use  of  $275  for  4  yr.  10  mo.  12  d.  from 
Jan.  12th,  1883,  what  amount  must  I  return  to  the  owner, 
allowing  6%  interest,  and  what  will  be  the  date  of  maturity  ? 


Interest.  107 


Six    Per    Cent 

Method. 

282.  At  6%  the  interest  of  $1 

For  1  yr.,     or  12  mo.,  is  6  cts.,  == 

.06      of  the  principal. 

For  £  yr.,     or    2  mo.,  is  1  ct.,    = 

.01      of  the  principal. 

For  T*¥  yr.,  or    1  mo.,  is  5  m.,    = 

.005    of  the  principal. 

For  ^  mo.,   or    6  d.,     is  1  m.,    = 

.001    of  the  principal. 

For  -jV  mo.,  or    Id.,    is  -J-  m.,    = 

.000£  of  the  principal. 

Hence,  the  following 

283.  Principles.— 1°.  The  interest  of  Si  at  6%,  is  half  as 
many  cents  as  there  are  months  in  the  given  time. 

2°.  The  interest  of  SI  at  6%,  is  one-sixth  as  many  mills  as 
there  are  days  in  the  given  time. 

1.  What  is  the  interest  of  $1250.26  for  1  yr.  3  mo.  21  d.,  at 
6%  ?    What  is  the  amount  ? 

Explanation.— The  int.  of  $1  for  15  m.  =  .075  $1250.26  Prin. 

By  2°,  int.  of  $1  for  21  d.         =  .0035  ^735  Int  $1 

Int.  of  $1  for  1  yr.  3  mo.  21  d.  =  .0785  625130 

As  the  interest  of  $1  for  the  given  time  and  10.00208 

rate  is  $.0785,  the  interest  of  $1250.26  must  be  Q7  *1  89 

$1250.26  x  .0785  =  $98.14541  interest.  — — - 

The  prin.  $1250.26  +  $98.14541 =$1348.40541,  $98.145410,   Ans. 
Amount.    Hence,  the 

Rule. — Multiply  the  principal  by  the  interest  of  $1 
for  the  given  time  and  rate. 

Notes. — 1.  When  the  rate  is  greater  or  less  than  6$,  find  the  interest 
of  the  principal  at  6%  for  the  given  time  ;  then  add  to  or  subtract  from  it 
such  a  part  of  itself,  as  the  given  rate  exceeds  or  falls  short  of  6  per  cent. 

2.  If  the  mills  are  5  or  more,  it  is  customary  to  add  1  to  the  cents  ;  if 
less  than  5,  they  are  disregarded. 

3.  Only  three  decimals  are  retained  in  the  following  Answers,  and  each 
answer  is  found  by  the  rule  under  which  the  Example  is  placed. 

4.  In  finding  the  interest  of  $1  for  days,  it  is  sufficient  for  ordinary 
purposes  to  carry  the  decimals  to  four  places. 


108  Percentage. 

2.  What  is  the  int.  of  $6395  for  18  mo.  29  d.,  at  7%  ? 

3.  What  is  the  int.  of  $2745.13  for  3  mo.  17  d.,  at  5%? 

4.  What  is  the  int.  of  $1237.63  for  18  mo.  3  d.,  at  8%  ? 

5.  Find  the  amount  of  $2835.20  for  2  mo.  3  d.,  at  7%. 

6.  Find  the  amount  of  $4356.81  for  13  mo.  10  d.,  at  §\%. 

7.  What  is  the  interest  of  $520  from  March  21,  1880,  to 
Dec.  30,  1882,  at  7%? 

8.  At  6  per  cent,  what  is  the  interest  of  $569.65  from 
August  10th,  1882,  to  Feb.  6th,  1884  ? 

9.  At  7  per  cent,  what  was  the  amount  due  on  a  note  of 
$385,  dated  March  15th,  1880,  and  payable  Sept.  18th,  1881  ? 

Find  the  int.  at  6%  Find  the  amount  at  6% 

10.  On  $842  for  2  yr.  8  mo.  13.  On  $850  for  3  yr.  5  mo. 

11.  On  $648  for  1  yr.  9  mo.  14.  On  $519  for  4  yr.  8  mo. 

12.  On  $952  for  3  yr.  5  mo.  15.  On  $1250  for  7  mo.  15  d. 

Method    by     Days. 

284.     l.  What  is  the  interest  of  $248.60  for  90  days,  at  6%  ? 

Analysts.— Since  the  int.  of  $1  at  6%  for  30  d.  is  $248.60     Prin. 
5  mills,  for  6  d.  it  is  1  mill,  or  ^  as  many  mills  as  days.  15     ^  d. 

Therefore,   multiplying  the   principal  by   $  of  the  124300 

number  of  days  will  give  the  interest  in  mills,  which  olefin 

are  changed  to  dollars  and  cents   by  moving  the  

decimal  point  3  places  to  the  left.     Hence,  the  3729.00     Mills. 

$3,729,  Am. 

Rule. — Multiply  the  principal  by  £  of  the  number  of 
days  and  divide  the  product  by  1000.    (Art.  264,  C.  G.  A.) 

Note.— If  there  is  a  fraction  in  finding  £  of  the  days,  it  may  be  avoided 
by  multiplying  by  the  whole  number  of  days,  and  dividing  the  product 
by  6000. 

What  is  the  interest  of  What  is  the  amount  of 

2.  $850  for  63  days  at  6$  ?  6.   $670  for  78  days  at  5%  ? 

3.  $945.50  for  33  days  at  6%  ?  7.  $785  for  45  days  at  7%  ? 

4.  $378.68  for  75  days  at  6%?  8.  $1200  for  68  d.  at  5%  ? 

5.  $354.75  for  130  days  at  6%  ?  9.  $2500  for  93  d.  at  8%  ? 


Interest  109 

10.  At  6  per  cent,  what  is  the  amount  due  on  a  note  of 
$391,  dated  Oct.  9th,  1881,  and  payable  March  1st,  1882  ?  • 

n.  At  5  per  cent,  what  is  the  amount  of  $623  from  Feb. 
19th,  1883,  to  Aug.  10th,  1883  ? 

Bankers'     Method. 

285.  A  contraction  often  used  by  hankers  and  others  in 
finding  the  interest  on  any  number  of  dollars  at  6%  for  60  days, 
is  illustrated  in  the  following  example : 

12.  Find  the  interest  of  $2835.20  for  2  mo.  3  d.,  at  6%. 

Explanation.  —  From    the    right    of    the  operation. 

dollars,  cut  off  2  figures  ;  this  gives  the  int.  for  20  )  28  35.20 
60  d.  (2  mo.) ;  3d.  =  4  or  ^  of  60  d.;  there-  j  4^75 

fore,  $28.352-*- 20  =  $1.4176,  the  int.   for  3  d. 

These  results  added  together  give  the  int.  for  $29.^696,    A)IS. 

2  mo.  3  d.     Hence,  the 

Kule. — Cut  off  the  two  right-hand  figures  of  the  dollars 
for  60  days  interest  at  6%;  then  add  or  subtract  the 
fractional  -part  of  60  days  interest  indicated  by  the  time. 

Notes. — 1.  The  same  rule  is  applicable  where  the  time  is  a  multiple 
of  60. 

2.  The  interest  at  other  rates  is  found  as  in  other  6%  methods. 

13.  What  is  the  interest  of  $360  for  95  d.,  at  6%  ? 

Explanation. —  Since    95    days    equals  95  d.  —  60 -J- 30 +  5 

60  +  30  +  5  days,  and  30  is  $  of  60,  the  int.  for  2  )  $3  60  =  Int.  60  d. 

60  d.-s-  2  gives  the  int.  for  30  d.;  and  as  5d.        p  \    1  SO  "     30  d 

are  1-  of  30  d.  the  int.  for  30  d.  -r-  6  erives  the  ' 

int.  for  5  days.     The  sum  of  these  results  is  ou  —             °  a< 

the  answer.  $5^  Ans% 

Find  the  interest  at  6%  Find  the  interest  at  6% 

14.  On  $2500  for  75  days.  18.  On  $8360  for  78  days. 

15.  On  $750  for  48  days.  19.  On  $4780  for  51  days. 

16.  On  $6253  for  96  days.  20.  On  $3654  for  43  days. 

17.  On  $4525  for  47  days.  21.  On  $9875  for  153  days. 


110  Percentage. 

286.  Another  short  method  of  finding  the  interest  on  cer- 
tain sums,  at  different  per  cents  is  explained  in  the  use  of  the 
following  table  giving  the  various  sums  on  which  the  interest 
at  the  per  cents  named,  is  one  cent  per  day.    Thus, 


$90  at  ±%. 

$40  at  1\%. 

$24  at  15#. 

$80   "   *$%. 

$45   "  8%. 

$20   «  18%. 

$72   "   5%. 

$40   "  9%. 

$50   "  &%. 

$60   "   6%. 

$36   "  10^. 

$70   «  ^. 

$52  "   7%. 

$30   "  12%. 

$35   «  H%. 

Note. — This  table  if  committed  to  memory  will  be  found  very  useful, 
particularly  when  the  days  are  not  aliquot  parts  of  a  year. 

22.  Find  the  interest  on  $72,  at  5%,  for  3  mo.  18  days. 

Explanation. — Since  the  int.  on  $72,  at  3  mo.  18  d.  =  108  da. 
5%,  by  the  table,  is  1  cent  per  day,  for  108  d.  fo]  OP,     An* 

it  is  108  cts.,  or  $1.08.     Hence,  the  f         ' 

Hulk.— Point  off  the  two  right-hand  -figures  of  the  days, 
for  cents ;  the  result  is  the  interest  for  the  given  time  of 
the  several  sums  found  in  the  table,  at  the  %  attached. 

Notes.— 1.  This  method  may  be  applied  to  any  multiple  or  fraction  of 
the  several  sums  given  in  the  table.  If  the  days  are  less  than  10  a  cipher 
should  be  prefixed  before  pointing  off. 

2.  The  first  contraction  is  based  on  the  fact  that  the  interest  on 
$1,  at  6  °/o  for  60  d.  is  1  cent.  The  second  on  the  fact  that  on  given  sums 
at  given  rates  the  int.  is  as  many  cents  as  days. 

23.  What  is  the  int.  of  $240,  at  6%,  for  1  yr.  2  mo.  15  d.? 

Explanation.— Since  $240  =  4  1  yr.  ==  360  d. 

times  $60,  the  int.  of  $60  for  the 
time  must  be  multiplied  by  4.  The 
given  time  =  360  +60  +  15  d.,  or 
435  days.  Cutting  off  two  figures 
gives  the  int.  of  $60  =  $4.35,  and 
$4.35  x  4  =  $17.40. 

24.  Int.  $270  at  4=%,  280  d.  ? 

25.  $3280  at  fy%,  358  d.  ? 

26.  $3672  at  lb%,  869  d.  ? 


2  mo. 

15  d.  = 

75  d. 

$4 

35  =  Int.  $60 
4 

$17.40,  Ans. 

27. 

$104,845  d.,at  1%? 

28. 

$684,  395  d.,  at  8^? 

29. 

$320,  76 

3  d.,  at  9%  ? 

Interest  m 


Accurate     Interest. 

287.  The  methods  based  upon  the  supposition  that  360  days 
make  a  year  and  30  days  a  month,  though  common,  are  not 
strictly  accurate.  As  a  year  contains  365  days,  the  interest 
found  by  these  methods  is  ^f-,  or  ^  part  of  itself  too  large. 

288.  To  compute  Accurate  Interest. 

1.  What  is  the  exact  interest,  at  6%,  of  $2486.50  for 
93  days? 

Explanation. — The  interest  at  6%  is  $38.54,  -^  part  of  which  is  $.53, 

and  $38.54- $.53  =  $38.01,  Am.     Hence,  the 

Eule. — Find  the  interest  by  the  6%  method  and  sub- 
tract from  it  YL3  part  of  itself. 

2.  What  is  the  exact  interest  of  $8568  for  93  d.,  at  6%  ? 

3.  What  is  the  exact  interest  of  $5200  for  123  d.,  at  1f0? 

4.  Find  the  accurate  interest  of  $4560  for  120  d.,  at  7%? 

5.  Find  the  accurate  interest  of  $16485  for  133  d.,  at  6%  ? 

6.  Find  the  accurate  interest  of  $36720  for  63  d.,  at  5%  ? 

7.  What  is  the  exact  interest  on  a  note  for  $5800  from  Jan. 
15,  1882,  to  July  4,  1882,  at  6%  ? 

289.  Interest  on  U.  S.  Bonds  is  computed  on  the  basis  of 
365  days  to  a  year ;  hence,  for  any  number  of  days  less  than  a 
year,  take  a  corresponding  fractional  part  of  1  year's  interest. 
Thus,  for  27  d.  take  -gfa,  etc. 

Note. — According  to  this  rule  the  interest  of  $100  at  3^  per  cent  for 
1  day  is  1  cent.  At  twice  3{^ %  =  7f^%,  or  7T3o%,  it  is  2  cents  a  day 
on  $100.  This  is  the  rate  of  interest  which  the  U.  S.  Seven-thirty 
Treasury  Notes  bore,  and  from  which  they  took  their  name. 

Find  the  exact  interest,  at  4=%,  5%,  and  7%  of 

8.  $842,  105  d.  11.   $1600,  192  d. 

9.  $1250,  126  d.  12.  $2500,  230  d. 
10.  $1728,  160  d.                      13.  $8500,  183  d. 


112  Percentage. 


ANNUAL     INTEREST. 

290.  Annual  Interest  is  interest  that  is  payable  every  year. 

Note. — When  notes  are  made  payable  "  with  interest  annually,"  sim- 
ple interest  can  be  collected,  in  most  of  the  States,  on  the  annual  interest 
after  it  becomes  due.  This  is  according  to  the  contract,  and  is  an  act  of 
justice  to  the  creditor,  to  compensate  him  for  the  damage  he  suffers  by 
not  receiving  his  money  when  due. 

291.  To  Compute  Annual  Interest,  when  the  Principal,  Rate, 
and  Time  are  given. 

1.  What  is  the  amount  due  on  a  note  of  $5000,  at  6%,  in 
3  yr.  with  interest  payable  annually  ? 

SOLUTION. 

Principal $5000.00 

Interest  for  1  year  is  $300 ;  for  3  years  it  is  $300  x  3,  or 900.00 

Interest  on  1st  annual  interest  for  2  yr.  is 36.00 

2d        "  M        "    1"    is 18.00 

The  amount  is $5954.00 

Eule. — Find  the  interest  on  the  principal  for  the  given 
time  and  rate;  also  find  the  simple  legal  int.  on  each 
annual  int.  for  the  time  it  has  remained  unpaid. 

The  sum  of  the  principal  and  its  int.,  with  the  int.  on 
the  unpaid  annual  interests,  will  be  the  amount. 

Note. — When  notes  are  made  for  long  periods  on  collateral  security, 
moneyed  institutions  sometimes  take  a  bond  and  mortgage  for  the 
principal  without  interest,  and  take  notes  maturing  at  the  time  each 
annual  interest  is  payable.  These  notes  are  entitled  to  interest  after 
maturity,  like  any  other  note,  and  may  be  collected  without  disturbing 
the  original  loan. 

2.  What  is  the  amount  of  a  note  of  $2500  payable  in  4  yr. 
3  mo.  12  d.  with  interest  annually  at  5%  ? 

3.  What  will  be  the  amount  due  on  a  note  of  $2375,  at  6% 
annual  interest,  payable  in  4  yr.  6  mo.  15  d.  if  no  payments  are 
made? 

4.  At  h%  annual  interest,  how  much  will  be  due  on  a  note 
of  $12648  in  5  years,  no  payments  having  been  made  ? 


Problems  in  Interest.  113 

5.  At  6%  annual  interest,  what  will  be  the  amount  of  a  loan 
of  $15000  in  3  years,  if  notes  from  date  with  semi-annual 
interest  are  given  ? 

6.  At  7$,  what  would  be  the  amt.  of  the  same  loan  ? 

Problems    in     Interest. 

292.  To  find  the  Mate,  when  the  Principal,  Interest,  and  Time 
are  given. 

1.  At  what  rate  of  interest  must  $828  be  loaned,  to  gain 
$47.61  in  1  year  3  months  and  10  days  ? 

Analysis.— At  1%    the  interest  of  •    $828  X  .01  =  $8.28 

$828,  is  $8.28  for  1  yr.    The  int.  for        3  mo   _  i  yr    _     2  07 
3mo.,  }yr.,isitheint    for  1  yr.,  and  ^  ^  ' 

the  int.  for  10  d.  is  ^  the  int.  for  one  6  

mo.     Since  the  int.  at  1%  is  $10.58  for  $10.58 

the  time,  $47.61  is  as  many  times  1%       la58  )  $47.61  (  4J^,   Am. 
int.  as  $10.58  are  contained    times  in 
$47.61,  or  4 1  times.    Hence,  the 

Rule. — Divide  the  given  interest  by  the  interest  of  the 
principal,  at  1  per  cent  for  the  time. 

Formula. — Rate  =  Interest  -f-  (Prin.  x  1%  X  Time). 

Note. — When  the  amount  is  given  the  principal  and  interest  may  be 
said  to  be  given.  For,  the  amt.  =  the  prin.  +  int. ;  hence,  amt.— int.  =  the 
prin. ;  and  amt.— prin.  =  the  interest. 

2.  At  what  rate  will  $300  yield  $18  int.  in  9  months  ? 

3.  At  what  rate  will  $500  yield  $34  in  1  yr.  1  mo.  18  d.  ? 

4.  At  what  rate  will  $8450  yield  $148  int.  in  3  months? 

5.  At  what  per  cent  will  $1704  amount  to  $1870.42  in  1  yr. 

7  mo.  16  days? 

6.  At  what  per  cent  will  $311.50  amt.  to  $336.42  in  1  yr.  4  mo.? 

7.  Required  the  rate  of  int.  at  w7hich  $1728  yields  $84  in 

8  mo.  10  d. 

8.  At  what  %  will  $7300  yield  $147.46  in  4  yr.  5  mo.  26  d.? 

9.  At  what  %  will  $556  yield  $95.91  iu  3  yr.  5  mo.  12  d.? 

8 


114  Percentage. 

10.  An  investment  of  $7226.28  yields  $744.7937  per  year; 
what  is  the  rate  ? 

293.  To  find  the  Principal,  when  the  Interest,  Rate,  and  Time 
are  given. 

11.  What  principal  at  6%  will  yield   $450.66   int.  in  3  yr. 
6  mo.? 

Analysis. — The  int.  of  $1  for  3  yr.  6  mo.  at  6%  is  operation. 

$0.21,  therefore  $450.66  must  be  the  int.  of  as  many  .21  )  450.66 

dollars  as  $.21  are  contained  times  in  $450.66,  or  $2146.  A         &oT7« 

Hence,  the  jlnS'  ^i4b 

Eule. — Divide  the  -given  interest  by  the  interest  of  $1 
for  the  given  time  and  rate. 

Formula.— Principal  =  Interest  -~  (Rate  x  Time). 

12.  What  principal  will  yield  $1250  a  year,  at  6%  interest  ? 

13.  A  professorship  was  founded  with  a  salary  of  $3500  a 
year  ;  what  sum  was  invested  at  6%  to  produce  it  ? 

14.  What  sum  must  be  invested  at  6%  that  a  young  lady 
now  18  may  have  $10000  when  she  is  21  ? 

15.  What  principal  at  6%  per  annum  yields  6  cts.  a  day  ? 

294.  To  find  the  Principal,  when  the  Amount,  Rate,  and  Time 
are  given. 

16.  What  principal  at  6%  will  amount  to  $287.50  in  2  yr. 
6  months  ? 

Explanation.— The  amount  of  $1  for  2  yr.       1.15  )  287.50 

6  mo.  at  6%  is  $1.15,  and  $287.50-h  $1.15  =  $250.  ZZTZ 

Hence,  the  ^&U>   AnS' 

Rule. — Divide  the  given  amount  by  the  amount  of  $1 
for  the  given  time  and  rate. 

17.  What  sum  loaned  at  1%  a  month  will  amount  to  $600 
in  1  year  ? 

18.  What  principal  at  7%,  loaned  from.  Apr.  9th,  1881,  to 
Sept.  5,  1883,  will  amount  to  $1477.59  ? 


Problems  in  Interest.  115 

19.  What  sum  at  1%  will  amt.  to  $221.07  in  3  yr.  4  mo.  ? 

20.  What  principal  at  9%  will  amt.  to  $286  in  3  yr.  4  mo.  ? 

21.  What  principal  at  6%  will  amount  to  $3695.04  in  1  yr. 
4  mo.  18  days  ? 

22.  What  principal  at  8%  will  amount  to  $442.71  in  2  yr. 
2  mo.  24  days  ? 

295.  To  find  the  Time,  when  the  Principal,  Interest,  and  Rate 
are  given. 

23.  In  what  time  will  $1500  gain  $198  at  6%? 
Analysis.— The  int.  of  $1500  for  1  yr.  at  6%  is  operation, 

$90  ;  hence,  to  gain  $198  will  require  the  same  prin-       90  )  $198.00 
cipal  as  many  years  as  $90  are  contained  times  in  77T     jT'o'vj. 

$198  ;  and  $198-=-$90  =  2.2,  or  ty  years.     Hence,  the  '.     *     *  " 

Eule. — Divide  the  given  interest  by  the  interest  of  the 
principal  for  1  year  at  the  given  rate. 

Formula. — Time  =  Int.  -^  (Prin.  x  Rate). 

Notes. — 1.  If  the  quotient  contains  decimals,  reduce  them  to  months 
and  days.     (Art.  153.) 

2.  If  the  amount  is  given  instead  of  the  principal  or  the  interest,  find 
the  part  omitted,  and  proceed  as  above. 

3.  At  100%,  any  sum  will  double  itself  in  1  year  ;  therefore,  any  per 
cent  will  require  as  many  years  to  double  the  principal,  as  the  given  per 
cent  is  contained  times  in  100%. 

24.  In  what  time  will  $850  gain  $29.75  at  7$  ? 

25.  In  what  time  will  $273.51  amount  to  $312,864  at  7%? 

26.  In  what  time  will  $240  amount  to  $720,  at  \%%  ? 

27.  A  man  received  $236.75  for  the  use  of  $2820,  which  was 
Q>%  interest  for  the  time  ;  what  was  the  time  ? 

28.  How  long  must  $204  be  on  interest  at  6%  to  amount 
to  $217.09? 

29.  How  long  will  it  take  $500  at  5%  to%  gain  $500  interest ; 
that  is,  to  double  itself  ? 

OPERATION. 

Explanation.— The  interest  of  $500  for  1  year  at  5  % ,       25  )  500 

is  $25  ;  and  $500-*-$35  =  20.     Ans.  2$  years.  ' 

Ans.  20  yr. 


116 


Percentage. 
Tab  le. 


Showing  in  what  time  any  given  principal  will  double  itself 
at  any  rate,  from  1  to  20  per  cent  Simple  Interest. 


Per  cent. 

Years. 

Per  cent. 

Years. 

Per  cent. 

Years. 

Per  cent. 

Years. 

1 

100 

6 

161 

11 

«¥r 

16 

H 

2 

50 

7 

14f 

12 

81 

17 

5tf 

3 

33i 

8 

12J 

13 

7* 

18 

H 

4 

25 

9 

11* 

14 

7* 

19 

5A 

5 

20 

10 

10 

15 

6* 

20 

5 

30.  How  long  will  it  take  $10000  to  gain  $5000,  at  6  per  cent 
interest  ? 

31.  A  man  hired  $15000  at  1%,  and  retained  it  till  it 
amounted  to  $25000  ;  how  long  did  he  have  it  ? 

32.  A  man  loaned  his  clerk  $25000,  and  agreed  to  let  him 
have  it  at  5%  till  it  amounted  to  $60000 ;  how  long  did  he 
have  it  ? 


PARTIAL     PAYMENTS. 

296.  Partial  Payments  are  payments  at  different  times  of 
parts  of  a  note  or  bond. 

297.  Indorsements  are  receipts  of  payments  written  on  the 
back  of  notes  and  bonds,  stating  the  amount  and  date  of  the 
payment. 

298.  To  compute  Interest  on  notes  and  bonds,  when  partial 
payments  have  been  made. 


$965-  New  York,  March  8th,  1880. 

l.   On  demand,  I  promise  to  pay  George  B.  Curtis,  or 
order,  Nine  Hundred  Sixty-jive  Dollars,  until  interest  at  7  per 


cent,  value  received. 


Heniiy  Bbowx, 


Partial  Payments.  117 

The  following  payments  were  indorsed  on  this  note : 

Sept.  8th,  1880,  received  $75.30. 
June  18th,  1881,  received  $20.38. 
March  24th,  1882,  received  $80. 

What  was  due  on  taking  up  the  note,  Feb.  9th,  1883  ? 

OPEBATION. 

Principal,  dated  March  8th,  1880 $965.00 

Int.  to  first  pay't,  Sept.  8th,  1880  (6  mo.) 33.775 

Amount  due  on  note  Sept.  8th. 998.775 

1st  pay't  (to  be  deducted  from  amt.) 75.30 

Remainder,  or  new  principal 923.475 

Int.  to  2d  pay't,  June  18th  (9  mo.  10  d.) 50.278 

2d  pay't  (less  than  int.  due) $20.38 

Int.  on  same  principal  from  June  18th  to  March  24th, 
1882  (9  mo.  6  d.) $49,559  -  $20.38  =  29.179 

Amount  due  March  24th,  1882 1002,932 

3d  pay't  (being  greater  than  the  int.  now  due)  is  to  be  deducted 

from  the  amount 80.00 

Balance  due  March  24th,  1882 922.932 

Int.  on  Bal.  to  Feb.  9th  (10  mo.  15  d.) 56.529 

Bal.  due  on  taking  up  the  note,  Feb.  9th,  1883 $979,461 

United    States    Rule. 

Find  the  amount  of  the  principal  to  the  time  of  the 
first  payment,  and  subtracting  the  payment  from  it,  find 
the  amount  of  the  remainder  as  a  new  principal,  to  the 
time  of  the  next  payment. 

If  the  payment  is  less  than  the  interest,  find  the 
amount  of  the  principal  to  the  time  ivhen  the  sum  of 
the  payments  equals  or  exceeds  the  interest  due;  and 
subtract  the  sum  of  the  payments  from  this  amount. 

Proceed  in  this  manner  to  the  time  of  settlement. 

Notes. — 1.  The  principles  upon  which  this  rule  is  founded  are, 
1st.   That    payments    must    be    applied    first    to    discharge    accrued 

interest,  and  then   the   remainder,  if  any,  toward  the  discharge  of  the 

principal. 

2d.  That  only  unpaid  principal  can  draw  interest. 


118  Percentage. 


$650-  Boston,  Jan.  1st,.  1882. 

2.  For  value  received,  I  promise  to  pay  John  Lincoln,  or 
order,  Six  Hundred  Fifty  Dollars  on  demand,  with  interest  at 
6  per  cent.  George  Law. 

Indorsed,  Aug.  13th,  1882,  $100. 
Indorsed,  April  13th,  1883,  $120. 

What  was  due  on  the  note,  Jan.  20th,  1884 ?  ^  ^9S.9  ^ 


Trenton,  April  10th,  1874. 


3.  Four  months  after  date,  I  promise  to  pay  James  Gar- 
field, or  order,  Two  Thousand  Four  Hundred  Sixty  Dollars, 
with  interest  at  6  per  cent,  value  received. 

George  G.  Williams. 

Indorsed,  Aug.  20th,  1875,  $840. 
Dec.  26th,  1875,  $400. 
May  2d,  1876,  $1000. 

How  much  was  due  Aug.  20th,  1876  ? 


$5000-  Indianapolis,  May  1st,  1875. 

4.  Six  months  after  date,  I  promise  to  pay  John  Folger,  or 
order,  Five  Thousand  Dollars,  with  interest  at  5 per  cent,  value 
received.  John  Adams. 

Indorsed,  Oct.  1st,  1875,  $700. 
Feb.  7th,  1876,  $45. 
Sept.  13th,  1876,  $480. 

What  was  the  balance  due  Jan.  1st,  1877  ? 

Mercantile    Method. 

299.  When  Partial  Payments  are  made  on  short  notes  or 
interest  accounts,  business  men  commonly  employ  the  follow- 
ing method : 

Find  the  amount  of  the  whole  debt  to  the  time  of  set- 
tlement;  also  find  the  amount  of  each  -payment  from 
the  time  it  was  made  to  the  time  of  settlement. 


Partial  Payments,  119 

Subtract  the  amount  of  the  payments  from  the  amount 
of  the  debt ;  the  remainder  will  be  the  balance  due. 

$■^16-  Rochester,  March  21st,  1880. 

5.  On  demand,  I  promise  to  pay  to  the  order  of  Henry 
Patton,  Four  Hundred  Sixteen  Dollars,  with  interest  at  7  per 
cent,  value  received.  Johk  Martin. 


Keceived  on  the  above  note  the  following  sums : 

June  15th,  1880,  $35.00. 
Oct.  9th,  1880,  $23.00. 
Jan.  12th,  1881,  $68.00. 

What  was  due  on  the  note,  Sept.  21st,  1881  ? 

SOLUTION. 

Principal,  dated  March  21st,  1880 $416,000 

Int.  to  settlement  (1  yr.  6  mo.),  at  7% 43.680 

Amount,  Sept.  21st,  1881 459.680 

1st  pay't,  $35.00,  Time  (1  yr.  3  mo.  6  d.),  Amount $38,103 

2d  pay't,  $23.00,  Time  (11  mo.  12  d.),  Amount 24.530 

3d  pay't,  $68.00,  Time  (8  mo.  9  d.),  Amount 71.292 

Amount  of  the  payments 133.925 

Balance  due  Sept.  21st,  1881 $325,755 

6.  A  bill  of  goods  amounting  to  $850,  was  to  be  paid  Jan. 
1st,  1880.  Received  June  10th,  $145 ;  Sept.  23d,  $465  ;  Oct. 
3d,  $23 ;  what  was  due  on  the  bill  Dec.  31st,  1880,  int.  6%  ? 

7.  An  account  of  $3200  due  March  3d,  received  the  follow- 
ing payments:  June  1st,  $310;  Aug.  7th,  $219  ;  Oct.  17th, 
$200  ;  what  was  due  on  the  27th  of  the  following  December, 
allowing  7%  interest  ? 

300.   Connecticut  Rule  for  Partial  Payments. 

I.  When  the  first  payment  is  a  year  or  more  from  the  time 
the  interest  commenced : 

Find  the  amount  of  the  principal  to  that  time.  If  the 
payment  equals  or  exceeds  the  interest  due,  subtract  it 
from  the  amount  thus  found,  and  considering  the  re- 
mainder a  new  principal,  proceed  as  before. 


120  Percentage. 

II.  When  a  pay't  is  made  before  a  year's  int.  has  accrued : 

Find  the  amount  of  the  principal  for  1  year ;  also,  if 
the  payment  equals  or  exceeds  the  interest  due,  find  its 
amount  from  the  time  it  was  made  to  the  end  of  the 
year ;  then  subtract  this  amount  from  the  amount  of  the 
principal,  and  treat  the  remainder  as  a  new  principal. 

III.  If  the  payment  be  less  than  the  interest: 

Subtract  the  payment  only  from  the  amount  of  the 
principal  thus  found,  and  proceed  as  before. 

$650'  New  Haven,  April  12th,  1879. 

8.  On  demand,  I  promise  to  pay  to  the  order  of  George 
Selden,  Six  Hundred  Fifty  Dollars,  with  interest,  value 
received.  Thomas  Sawyer. 

Indorsed,  May  1,  1880,  rec'd  $116.20. 
Feb.  10,  1881,  rec'd  $61.50. 
Dec.  12,  1881,  rec'd  $12.10. 
•        June  20,  1882,  rec'd  $110. 

What  was  due  Oct.  21,  1882  ? 

SOLUTION. 

Principal,  dated  April  12,  1879. . . . , $650.00 

Interest  to  first  payment,  May  1,  1880  (1  yr.  19  da.) 41.06 

Amount,  May  1,  '80 691.06 

First  payment,  May  1,  '80 ...  116.20 

Remainder,  or  new  principal,  May  1,  '80 574.86 

Interest  to  May  1,  '81,  or  1  yr.  (2d  payment  being  short  of  1  yr.). .  34.49 

Amount,  May  1,  *81 609.35 

Amount  of  second  payment  to  May  1,  '81  (2  mo.  20  da.) 62.32 

Remainder,  or  new  principal,  May  1,  '81 547.03 

Amount,  May  1,  '82  (1  yr.) 579.86 

Third  payment  (being  less  than  interest  due)  draws  no  interest. . .       12.10 
Remainder,  or  new  principal,  May  1,  '82 567.76 

Amount,  Oct.  21,  '82  (5  mo.  20  da.) 583.85 

Amount  of  last  payment  to  settlement  (4  mo.  1  da.) 112.22 

Balance  due  Oct.  21,  '82 $471.63 


Partial  Payments.  121 

301.   Vermont  Rule  for  Partial  Payments. 

I.  When  payments  are  made  on  notes  bearing  interest,  such 
payments  shall  be  applied, 

"  First,  to  liquidate  the  interest  that  has  accrued  at  the 
time  of  such  payments ;  and  secondly,  to  the  extinguish- 
ment of  the  principal" 

II.  When  notes  are  made  "  with  interest  annually." 

The  annual  interests  ivhich  reviain  unpaid  shall  be 
subject  to  simple  interest  from  the  time  they  become  due 
to  the  time  of  settlement. 

III.  If  payments  have  been  made  in  any  year,  reckoning 
from  the  time  such  annual  interest  began  to  accrue,  the  amount 
of  such  payments  at  the  end  of  such  year,  with  interest  thereon 
from  the  time  of  payment,  shall  be  applied : 

"  First,  to  liquidate  the  simple  interest  that  has  accrued 
from  the  unpaid  annual  interests. 

"  Secondly,  to  liquidate  the  annual  interests  that  have 
become  due. 

"  Thirdly,  to  the  extinguishment  of  the  principal. 

H500-  Montpelier,  Feb.  1st,  1878. 

9.  On  demand,  I  promise  to  pay  to  the  order  of  Jared 
Sparks,  Fifteen  Hundred  Dollars,  with  interest  annually  at 
6%,  value  received.  Augustus  Morse. 

Indorsed,  Aug.  1,  1878,  $160.     Nov.  1,  1881,  $250. 

Eequired  the  amount  due  Feb.  1,  1882. 

SOLUTION. 

Principal $1500.00 

Annual  interest  to  Feb.  1,  '79  (1  yr.  at  6%) 90.00 

Amount 1590.00 

First  payment,  Aug.  1,  78 $160.00 

Interest  on  same  to  Feb.  1,  '79  (6  mos.) 4.80      164.80 

Remainder,  or  new  principal $1425.20 


122  Percentage. 

Remainder,  or  new  principal $1425.20 

Annual  interest  on  same  from  Feb.  1,  '79,  to  Feb.  1,  '82  (3  yr.). .  256.53 
Interest  on  first  annual  interest  from  Feb.  1,  '80  (2  yr.). .    $10.26 

Interest  on  second  annual  int.  from  Feb.  1,  '81  (1  yr.). . .         5.13  15.39 

Amount 1697.12 

Second  payment,  Nov.  1,  '81 $250.00 

Interest  on  same  to  Feb.  1,  '82  (3  mo.)  3.75  253.75 

Balance  due  Feb.  1,  '82 $1443.37 


302.    New  Hampshire  Rule  for  Partial  Payments.* 

I.  When  on  notes  drawing  annual  interest, 

Find  the  interest  due  upon  the  principal,  and  the 
annual  interest  at  the  annual  rest  \  next  after  the  first 
payment,  from  date  of  note. 

II.  If  the  first  pa)Tt.  be  larger  than  the  sum  of  interests  due, 

Find  the  int.  on  such  payt.  from  the  time  it  was  made 
to  end  of  the  year,  and  deduct  the  sum  of  payt.  and  int. 
from  the  amount  of  principal  and  interests. 

III.  If  less  than  the  annual  interests  accruing, 

Deduct  the  payment  without  interest  from  th  e  sum  of 
annual  and  simple  interest,  and  upon  the  balance  of 
such  interest  cast  the  simple  interest  to  the  time  of  the 
next  rest. 

IV.  If  less  than  the  simple  interest  due, 

Deduct  it  from  the  simple  interest,  and  add  the  bal- 
ance without  interest  to  the  other  interests  due  when  the 
next  payment  is  made. 

Proceed  thus  to  the  end  of  the  year  after  the  last  pay- 
ment, being  careful  to  carry  forward  all  interest  unpaid 
at  the  end  of  each  year. 


*  Abstract  of  N.  H.  Court  Rule.  Report  of  Hon.  C.  A.  Downs,  State  Superintendent, 
t  The  time  when  the  annual  interest  becomes  due  from  year  to  year. 


Partial  Payments.  123 

10.  A  agrees  to  pay  B  $2000  in  6  yr.  from  Jan.  1,  1870,  with 
interest  annually.  On  July  1,  1872,  a  payment  of  $500  was 
made;  and  Oct.  1,  1873,  $50.     What  was  due  Jan.  1,  1876  ? 

SOLUTION. 

Principal $2000.00 

First  year's  interest $120.00 

2  yr.  simple  int.  thereon 14.40      134.40 

Second  year's  interest 120.00 

1  yr.  simple  int.  thereon 7.20      127.20 

Third  year's  interest 120.00 

2381.60 

First  payment,  July  1,  1872 $500.00 

Int.  thereon  from  July  1,  '72,  to  Jan.  1,  '73 15.00      515.00 

Balance  of  principal $1866.60 

Interest  on  same  for  fourth  year. $111.99  + 

Second  pay't  (less  than  the  int.  accruing  during  the  year) 50.00 

Balance  of  fourth  year's  interest  unpaid 61.99  + 

Annual  interest  on  balance  of  principal  for  fifth  year 111.99  + 

"            "                 "                 "              sixth   "     111.99  + 

Simple  int.  on  unpaid  bal.  of  fourth  year's  int.  for  2  yr 7.43  + 

Simple  interest  on  fifth  year's  interest  for  one  year. 6.71  + 

Balance  of  principal 1866.60 

Amount  due  January  1,  1876 $2166.71 

303.   To  Compute  Interest  on  Sterling  Money. 

11.  What  is  the  int.  of  £175  10s.  6d.  for  1  yr.,  at  5  per  cent  ? 
Explanation.— Reduce  10s.  6d.  to  the  £175.525    Prin. 

decimal   of   a    pound    (Art.    154);    then  -05    Rate. 

multiply  the  principal   by  the  rate,  and  £8.77625     int.  1  year. 

point  off  the  product  as  before.     The  8  on 20 

the  left  of  the  point  is  pounds,  the  figures  15.52500  s. 

on   the   right   are  decimals  of  a  pound, 

which  must  be  reduced  to  shillings,  pence,  6.30000  d. 

and  farthings.     (Art.  153.)     Hence,  the  Ans.  £8  15s.  Q\d. 

Eule. — Reduce  the  given  shillings,  etc.,  to  the  decimal 
of  a  pound;  then  -proceed  as  in  TJ.  S.  money.  Reduce 
the  decimals  of  a  pound  in  the  result  to  shillings,  pence, 
and  farthings.     (Art.  153.) 

12.  What  is  the  int.  of  £56  15s.  for  1  yr.  6  mo.,  at  6%  ? 

13.  What  is  the  int.  of  £96  18s.  for  2  yr.  6  mo.,  at  A\%  ? 

14.  What  is  the  amt.  of  £100  for  2  yr.  4  mo.,  at  5%  ? 


124  Percentage. 


COMPOUND    INTEREST. 

304.  Compound  Interest  is  the  interest  of  the  principal  and 
of  the  unpaid  interest  after  it  becomes  due. 

305.  To  Compute  Compound  Interest,  when  the  Principal, 
Rate,  and  Time  of  compounding  it  are  given. 

I.  What  is  the  compound  interest  of  $5000  for  3  years, 
at  6%? 

Principal $5000 

Int.  for  1st  year,  $5000  x  .06 300 

Amt.  for  1  yr. ,  or  2d  prin 5300 

Int.  for  2d  year,  $5300  x  .06 318 

Amt.  for  2  yr.,  or  3d  prin 5618 

Int.  for  3d  year,  $5618  x. 06 337.08 

Amt.  for  3  years 5955.08 

Original  principal  to  be  subtracted 5000  00 

Compound  int.  for  3  years $955.08 

Hence,  the 

Eule. — I.  Find  the  amount  of  the  principal  for  the 
first  period.  Treat  this  amount  as  a  new  principal,  and 
find  the  amount  due  on  it  for  the  next  period,  and  so  on 
through  the  whole  time. 

II.  Subtract  the  given  principal  from  the  last  amount, 
and  the  remainder  will  be  the  compound  interest. 

Note. — If  there  are  months  or  days  after  the  last  regular  period  at 
which  the  interest  is  compounded,  find  the  interest  on  the  amount  last 

i obtained   for  them,   and    add    it  to  the  same,    before    subtracting    the 
principal. 
2.   What  is   the  compound  int.  of   $1450  for  3  yr.  6  mo., 
at  6%? 

3.  What  is  the  compound  int.  of  $8500  for  4  yr.  6  mo., 
at5%? 

4.  What  is  the  amt.  of  $9500  for  6  yr.  3  mo.,  at  b%,  com- 
pound int.  ? 


Compound  Interest 


125 


Table. 

306.  Showing  the  amount  of  $1,  at  3,  3|>  4,  5,  6,  and 
compound  interest,  for  any  number  of  years  from  1  to  20. 


n 


Yrs. 

3%. 

3|%. 

4%. 

5%. 

6%. 

Ifc 

1. 

1.030  000 

1.035  000 

1.040  000 

1.050  000 

1.060  000 

1.07  000 

2. 

1.060  900 

1.071  225 

1.081  600 

1.102  500 

1.123  600 

1.14  490 

3. 

1.092  727 

1.108  718 

1.124  864 

1.157  625 

1.191  016 

1.22  504 

4. 

1.125  509 

1.147  523 

1.169  859 

1.215  506 

1.262  477 

1.31  079 

5. 

1.159  274 

1.187  686 

1.216  653 

1.276  282 

1.338  226 

1.40  255 

6. 

1.194  052 

1.229  255 

1.265  319 

1.340  096 

1.418  519 

1.50  073 

7. 

1.229  874 

1.272  279 

1.315  932 

1.407  100 

1.503  630 

1.60  578 

8. 

1.266  770 

1.316  809 

1.368  569 

1.477  455 

1.593  848 

1.71  818 

9. 

1.304  773 

1.362  897  ;  1.423  312 

1.551  328 

1.689  479 

1.83  845 

10. 

1.343  916 

1.410  599  1.480  244 

1.628  895 

1.790  848 

1.96  715 

11. 

1.384  234 

1.459  970  1.539  451 

1.710  339 

1.898  299 

2.10  485 

12. 

1.425  761 

1.511  069 

1.601  032 

1.795  856 

2.012  196 

2.25  219 

13. 

1.468  534 

1.563  956 

1.665  074 

1.885  649 

2.132  928 

2.40  984 

14. 

1.512  590 

1.618  695 

1.731  676 

1.979  932 

2.260  904 

2.57  853 

15. 

1.557  967 

1.675  349 

1.800  944 

2.078  928 

2.396  558 

2.75  903 

16. 

1.604  706 

1.733  986 

1.872  981 

2.182  875 

2.540  §52 

2.95  216 

17. 

1.652  848 

1.794  676 

1.947  900 

2.292  018 

2.692  773 

3.15  881 

18. 

1.702  433 

1.857  489  2.025  817 

2.406  619 

2.854  339 

3.37  993 

19. 

1.753  506 

1.922  501  !  2.106  849 

2.526  950 

3.025  600 

3.61  652 

20. 

1.806  111 

1.989  789  !  2.191  123 

1 

2.653  298 

3.207  135 

3.86  968 

Note. — Compound  interest  cannot  be  collected  by  law  ;  but  a  creditor 
may  receive  it,  without  incurring  the  penalty  of  usury.  Savings  Banks 
pay  it  to  all  depositors  who  do  not  draw  their  interest  when  due. 

5.  What  is  the  compound  int.  and  amt.  of  $200  for  10  yr., 
at  3^? 

SOLUTION. 

Tabular  amount  of  $1  for  10  yr.,  at  U% $1.410599 

Multiply  by  the  prin 200 

Amt,  of  $200  for  10  yr 282.119800 

Subtracting  the  prin 200. 

Compound  int.  for  10  yr $82.1198 


126  Percentage. 

Eule. — I.  Multiply  the  tabular  amount  of  $1  for  the 
given  time  and  rate  by  the  principal ;  the  product  will 
be  the  amount. 

II.  From  the  amount  subtract  the  principal,  and  the 
remainder  will  be  the  compound  interest. 

Notes. — 1.  If  the  given  number  of  years  exceed  that  in  the  Table,  find 
the  amount  for  any  convenient  period,  as  half  the  given  years  ;  then  on 
this  amount  for  the  remaining  period. 

For  example,  the  amt.  for  20  years  by  table  .at  6%  =3.207135,  this 
multiplied  by  1.123600,  amt,  for  2  yr.  gives  $3.603537  the  amt.  for  22 
years. 

2.  If  interest  is  compounded  semi-annually  take  £  the  given  rate  and 
twice  the  number  of  years ;  if  compounded  quarterly,  take  \  the  given 
rate  and  4  times  the  number  of  years. 

Thus,  the  amount  of  $400  payable  semi-annually  for  3  yr.  at  6%,  is 
the  same  as  the  amt.  of  $400  for  6  yr,  at  3%,  payable  annually. 

6.  What  is  the  amt.  of  $3500  for  5  yr.,  at  5%  com.  interest? 

7.  What  is  the  amount  of  $1350  for  12  years,  at  1%  ? 
6.  What  is  the  com.  int.  of  $1469  for  15  years,  at  3%? 

9.  What  is  the  com.  int.  of  $2500  for  24  years,  at  6%  ? 

10.  What  is  the  com.  int.  of  $1650  for  30  years,  at  3£$? 

11.  What  is  the  amount  of  $1800  for  3  yr.,  at  6%  compound 
interest,  payable  semi-annually  ? 

V12.  What  is  the  amount  of  $1500  for  2  years,  at  12$  com- 
ound  interest,  payable  Quarterly? 

3.  To  find  the  principal  or  present  vvorth  of  an  amount  at  compound 
interest:  Divide  the  given  amount  by  the  amount  of  $1  for  the  given 
time  and  rate  at  compound  interest. 

13.  What  is  the  present  worth  of  $6036.25  due  in  8  years, 
at  Q%  compound  interest? 

14.  What  principal  at  compound  int.  will  amount  to 
$2375.92,  at  5%,  in  14  years? 

15.  What  is  the  present  worth  of  $2521.81,  due  in  14  years, 
at  6$  compound  interest  ? 

16.  What  principal  at  10$,  will  amount  to  $265.33  in  10 
years,  int.  payable  semi-annually  ? 


True  Discount.  127 

. 

TRUE    DISCOUNT. 

307.  Discount  is  a  deduction  from  a  stated  price,  or  from 
a  debt  paid  before  it  is  due. 

308.  The  Present  Worth  of  a  debt,  due  at  some  future  time 
without  interest,  is  the  sum  which  put  at  legal  interest  will 
amount  to  the  debt  when  it  becomes  due. 

309.  True  Discount  is  the  difference  between  the  face  of  a 
debt  and  its  present  worth. 

310.  To  find  the  Present  Worth  and  True  Discount  of  a  time 
note. 

1.  What  is  the  present  worth  and  true  discount  of  $478.06, 
due  in  1  year  and  8  mouths,  at  6%? 

Analysis.— The  amount  of  $1,  at  6%,  for  1  yr.  8  mo.  =  $1.10.  Since 
$1.10  is  the  amt.  of  $1,  at  6%  for  the  given  time,  $478.06  is  the  amt.  of 
as  many  dollars,  for  the  same  time  and  rate,  as  $1.10  is  contained  times  in 
$478.06,  and  $478.06 -^ $1.10  =  $434.60,  present  worth.  Then,  $478.06- 
434.60  =  $43.46,  the  true  discount.     Hence,  the 

Rule.— I.  Divide  the  debt  by  the  amount  of  $1  for  the 
given  time  and  rate ;  the  quotient  will  be  the  present 
woHh. 

II.  Subtract  the  present  worth  from  the  debt,  and  the 
remainder  will  be  the  true  discount. 

Find  the  present  worth  and  true  discount  of 

2.  $950.25,  due  in  1£  years,  at  6%. 

3.  $3272.50,  due  in  2  yr.  3  mo.,  at  7%. 

4.  $6895,  payable  in  3  years,  at  5.%. 

5.  $8650.75,  payable  in  3£  years,  at  ±\%. 

6.  $10000,  due  in  4  yr.  5  mo.,  at  %\%. 

7.  What  is  the  difference  between  the  interest  and  true  dis- 
count of  $52250,  for  1  year,  at  6%  ? 


128  Percentage. 

8.  If  a  note  for  $2500   be  given   with  interest  at  7%  per 
annum  for  G  mo.,  what  will  it  be  worth  3  mo.  from  date  ? 

9.  When  money  is  worth  6%,  which  is  preferable,  $15000 
cash,  or  $16000  payable  in  1  year  ? 


BANK    DISCOUNT. 

311.  Bank  Discount  is  simple  interest,  paid  in  advance. 

312.  The  Proceeds  of  a  note  are  the  part  paid  to  the  owner; 
the  Discount  is  the  part  deducted. 

313.  The  Maturity  of  a  note  or  draft  is  the  day  it  becomes 
legally  due.  In  most  States  a  note  does  not  mature  until  3 
days  after  the  time  named  for  its  payment. 

These  three  days  are  called  Days  of  Grace. 

Notes. — 1.  As  interest  is  charged  by  some  banks  for  the  day  of  dis- 
count as  well  as  for  the  day  of  maturity,  this  with  the  3  days  grace  makes 
the  time  for  which  discount  is  taken  four  days  more  than  the  time  named 
in  the  note. 

2.  If  the  last  day  of  grace  occurs  on  Sunday  or  a  legal  holiday,  the  note 
matures  on  the  preceding  business  day.  Thus,  if  a  note  matures  on 
Monday,  and  that  is  a  holiday,  it  is  payable  on  Saturday. 

314.  The  Term  of  Discount  is  the  time  from  the  date  of 
discount  to  the  maturity  of  the  note. 

Note. — In  computing  interest  and  discount  on  notes  and  drafts  the 
practice  is  not  uniform  as  to  what  constitutes  a  year.  Some  compute  it 
on  the  basis  of  360,  and  others  of  365  days  to  a  year.  On  Stock  loans  in 
Wall  Street,  interest  is  computed  on  the  basis  of  360  days  to  a  year. 

315.  To  find  the  Bank  Discount  and  Proceeds,  when  the 
Face  of  a  note,  Rate,  and  Time  are  given. 

l.  What  is  the  bank  discount  of  $568  for  3  mo.,  at  6%  ? 
What  are  the  proceeds  ? 

Solution. — The  face  of  the  note  =      $568 

Int.  of  $1  for  3  mo.  and  grace  at  6%  =     .0155 

Discount  =  $8,804 

Proceeds,  $568-$8.804  =  ^559.196.  Hence,  the 


Commercial  Paper.  129 

Rule. — Find  the  interest  of  the  note  at  the  given  rate 
for  three  days  more  than  the  specified  time ;  the  result 
is  the  discount. 

Subtract  the  discount  from  the  face  of  the  note ;  the 
remainder  will  be  the  proceeds. 

Note. — If  a  note  is  on  interest,  find  its  amount  at  maturity,  and  taking 
this  as  the  face  of  the  note,  cast  the  interest  on  it  as  above. 

2.  Find  the  proceeds  of  a  note  of  $850,  due  in  3  mo.,  at  6%  ? 

3.  Find  the  proceeds  of  a  draft  of  $885,  on  60  days,  at  6%. 

4.  Find  the  maturity,  the  term  of  discount  and  the  proceeds 
of  a  note  of  $5250,  on  60  days,  dated  July  1st,  1880,  and 
discounted  Aug.  21st,  1880,  at  5%. 

5.  Find  the  difference  between  the  true  and  bank  discount 
on  $6000  for  1  year,  allowing  each  3  days  grace,  at  7%  ? 

6.  A  merchant  bought  $6800  worth  of  goods  for  cash,  sold 
them  on  4  months,  at  15$  advance,  and  got  the  note  dis- 
counted at  6%  to  pay  the  bill.     How  much  did  he  make  ? 

316.  To  find  the  Face'  of  a  note,  that  the  proceeds  may 
amount  to  a  given  sum,  when  the  Rate  and  Time  are  given. 

7.  For  what  sum  must  a  note  be  made  on  4  months,  that 
the  proceeds  may  be  $6400,  discounted  at  6%? 

Solution.— The  bank  discount  of  $1  for  4  mo.  3  d.  =  $.0205 

The  proceeds  of  $1  =  $l-$.0205  =  $.9795 

Therefore,         The  face  of  the  note  is  $6400 -=-$.9795  =  $6533.945 
Hence,  the 

Rule. — Divide  the  given  sum  by  the  proceeds  of  $1  for 

,p.  (St.iip.ti,  f.i.m.p,  n.n.rl,  vn+.p 


the  given  time  and  rate 


8.  What  must  be  the  face  of  a  note  on  6  months,  discounted 
at  7%  that  the  proceeds  may  be  $900  ? 

9.  The  avails  of  a  note  were  $8350.90,  the  term  3  months, 
and  the  rate  of  discount  8%  ;  what  was  the  face  of  the  note  ? 

io.  How  large  a  note  on  90  days  must  I  have  discounted  at 
6$,  to  realize  $5460  ready  money  ? 
9 


130  Percentage. 

317.  To  find  the  face  of  a  draft  that  may  be  bought  for  a 
specified  sum,  when  the  per  cent  premium  or  discount  is  given. 

1.  How  large  a  draft  can  be  bought  for  $2040,  at  2% 
premium  ? 

Solution  —At  2%  premium,  $1.02  will  buy  $1  draft. 
Aud  $2040h- $1.02  =  2000.     Ans.  $2000. 

2.  How  large  a  draft  can  be  bought  for  $2910,  at  3% 
discount  ? 

Solution.— At  3%  discount,  $0.97  will  buy  $1  draft. 

And  $2910^.97  =  $3000,  Ant.    Heuce,  the 

Eule. — Divide  the  given  sum  by  $1  increased  or 
diminished  by  the  rate  of  premium  or  discount. 

3.  How  large  a  draft  on  San  Francisco  can  be  bought  for 
$5200,  at  a  premium  of  2-J$  ? 

4.  What  is  the  face  of  a  draft  on  Chicago  for  which  you  pay 
$8250,  at  \\%  discount  ? 

5.  A  merchant  invests  the  proceeds  of  a  sale,  amounting  to 
$3250,  in  a  draft  on  Chicago,  which  he  can  buy  at  a  discount 
of  \\% ;  how  large  is  the  draft  ? 

6.  What  is  the  face  of  a  draft  on  New  York  which  costs 
$2850,  at  \\%  premium  ? 


COMMERCIAL     OR    BUSINESS     PAPER. 

318.  Commercial  or  Business  Paper  includes  Promissory 
Notes,  Drafts,  Bills  of  Exchange,  etc. 

319.  A  Note  or  Promissory  Note  is  a  written  promise  to 
pay  a  certain  sum  on  demand  or  at  a  specified  time. 

Notes. — 1.  A  note  should  always  contain  the  words  "  value  received  ; " 
otherwise  it  is  not  valid,  and  the  holder  may  be  obliged  to  prove  it  was 
given  for  a  consideration,  in  order  to  collect  it. 

2.  A  note  as  a  gift  is  void  from  want  of  a  consideration,  unless  it  has 
passed  for  value  into  the  hands  of  an  innocent  third  party. 


Commercial  Paper.  131 

320.  The  Maker  of  a  note  or  draft  is  the  person  who 
signs  it. 

The  Payee  is  the  person  to  whom  it  is  to  be  paid. 

The  Holder  is  the  person  who  has  the  note  or  draft  in  his 
possession. 

Note. — A  note  becomes  void  when  founded  upon  fraud,  or  when  any 
material  alteration  is  made,  as  in  the  date,  amount,  or  time  of  payment. 

321.  A  Collateral  Note  is  one  given  with  stocks  or  other 
security,  empowering  the  holder  to  sell,  if  the  note  should  not 
be  paid  when  it  becomes  due. 

322.  A  Joint  Note  is  one  signed  by  two  or  more  persons. 

Notes. — 1.  The  Face  of  a  Note  is  the  sum  whose  payment  is 
promised.  This  sum  should  be  written  in  words  in  the  body  of  the  note, 
and  in  figures  at  the  top  or  bottom. 

2.  When  a  note  is  to  draw  interest  from  its  date,  it  should  contain 
the  words  "  with  interest ; "  otherwise  no  interest  can  be  collected.  For 
the  same  reason,  when  it  is  to  draw  interest  from  a  particular  time  after 
date,  that  fact  should  be  specified  in  the  note. 

3.  All  notes  are  entitled  to  legal  interest  after  they  become  due,  whether 
they  draw  it  before,  or  not. 

323.  A  Negotiable  Note  is  a  note  drawn  for  the  payment  of 
money  to  "order  or  bearer,"  without  any  conditions. 

A  Non-Negotiable  Note  is  one  which  is  not  made  payable  to 
"order  or  bearer,"  or  is  not  payable  in  money. 

Notes. — 1.  A  note  payable  to  A.  B.,  or  "order,"  is  transferable  by 
indorsement;  if  to  A.  B.,  or  "bearer,"  it  is  transferable  by  delivery. 
Treasury  notes  and  bank  bills  belong  to  this  class. 

2.  If  the  words  "  order"  and  "  bearer"  are  both  omitted,  the  note  can 
be  collected  only  by  the  party  named  in  it,  and  is  not  negotiable. 

3.  When  a  note  is  given  for  any  number  of  months,  calendar  months 
are  always  to  be  understood. 

4.  If  a  note  is  payable  on  demand,  it  is  legally  due  as  soon  as 
presented.  If  no  time  is  specified  for  the  payment,  it  is  understood  to  be 
on  demand. 


132  Percentage. 

5.  If  a  note  has  been  lost  or  destroyed  by  fire  or  other  accident,  its 
amount  may  be  collected  upon  sufficient  proof. 

324.  An  Indorser  is  a  person  who  writes  his  name  on  the 
back  of  a  note  and  becomes  security  for  its  payment. 

Notes.— 1.  If  an  indorser  of  a  note,  draft,  etc.,  does  not  wish  to  guar- 
antee its  payment,  he  writes  "  without  recourse  "  over  his  name  at  the  time 
of  the  indorsement.     This  does  not  affect  the  negotiability  of  the  note. 

2.  Sometimes  notes  and  drafts  are  drawn  to  the  order  of  the  maker,  to 
facilitate  their  transfer  without  the  indorsement  of  the  holder.  Such 
notes  are  negotiable  by  delivery. 

325.  An  Indorsement  is  the  signature  of  a  person  written 
upon  the  back  of  notes  and  other  commercial  instruments. 
(Art.  297.) 

Notes. — 1.  A  note  made  payable  to  A.  B.,  or  order,  may  be  collected  by 
any  one  to  whom  A.  B.  may  order  it  to  be  paid.  This  order  is  written  on 
the  back  of  the  note  and  is  called  an  indorsement. 

2.  If  A.  B.  writes  his  name  only  on  the  back  of  the  note,  it  is  an 
indorsement  in  blank,  and  is  equivalent  to  "  Pay  the  bearer." 

3.  All  the  parties  who  write  their  names  on  a  note  are  liable  for  the 
amount  due,  but  only  one  satisfaction  can  be  recovered. 

4.  No  days  of  grace  are  allowed  in  Alabama,  Georgia,  Kentucky, 
or  California,  except  the  note  is  held  by  a  private  banker  or  by  a  bank. 

326.  A  Draft  is  a  written  order  addressed  by  one  person  to 
another,  directing  him  to  pay  a  specified  sum  of  money  to  a 
third  person,  or  to  his  order. 

Notes. — 1.  A  person  accepts  or  promises  to  pay  a  draft,  by  writing  the 
word  accepted  across  the  face,  with  the  date  and  his  name  under  it. 
2.  To  honor  a  draft  is  to  accept  or  pay  it  on  presentation. 

327.  A  Protest  is  a  written  statement  made  by  a  notary 
public,  that  a  note  or  draft  has  been  duly  presented  by  the 
holder-  in  person  for  payment  or  acceptance,  and  was  refused. 
It  protests  against  the  Maker,  Drawer,  Drawee,  Acceptor, 
Payor,  Indorser,  etc.,  for  all  interest  costs  or  damages  incurred 
through  refusal  of  payment  thereof. 

Note. — A  protest  must  be  made  out  the  day  the  note  or  draft  matures, 
and  sent  to  the  indorser  immediately,  to  Jiold  him  responsible. 


Commercial  Paper.  133 

Forms    of    Notes    and    Drafts. 
328.    No.  I. — Time  Notes  without  Interest.    (Negotiable.) 


$850. 


New  York,  Jan.  10th,  1883. 


Tliree  months  after  date,  I  promise  to  pay  George  Ban- 
croft, or  order,  Three  Hundred  Fifty  Dollars,  value  received. 

Henry  Lincoln. 


What  are  the  bank  discount  and  proceeds  of  this  note  ? 

Note. — When  no  rate  of  interest  is  mentioned,  the  legal  rate  ( 
ate  is  always  understood. 

329.    No.  2.— Time  Notes  bearing  Interest.    (Negotiable.) 


$500'  Philadelphia,  Feb.  15th,  1883. 

Sixty  days  after  date,  we  promise  to  pay  H.  Foot,  or  order, 
Five  Hundred  Dollars,  with  interest,  without  defalcation,  value 
received.  John  Richards  &  Co. 

Required  the  bank  discount  and  proceeds. 

Notes. — 1.  When  banks  discount  time-notes  bearing  interest,  it  is  cus- 
tomary for  them  to  compute  the  interest  till  maturity,  and  take  the 
amount  as  the  face  of  the  note. 

2.  In  Penn.  negotiable  notes  must  contain  the  words  "  without  defalca- 
tion." In  New  Jersey  they  contain  the  words  "  without  defalcation  or 
discount." 

330.   No.  3. — Demand  Notes.    (Negotiable.) 


$1200-  Chicago,  April  15th,  1883. 

On  demand,  I  promise  to  pay  W.  H.  Seward,  or  bearer, 
Tivelve  Hundred  Dollars,  value  received. 

Daniel  Webster. 

What  was  due  on  the  above  note  June  21st,  at  8%  ? 

4.  What  would  be  its  amount  at  H%  ?    At  5%  ? 

Notes. — 1.  Notes  on  demand  are  entitled  to  the  legal  interest  of  the 
State  in  which  they  are  made  from  their  date  to  their  payment. 

2.  If  the  words  "or  bearer"  were  omitted,  the  above  note  would  not 
be  negotiable. 


134  Percentage. 

331.    No.  5.— Notes  without  Grace.    (Negotiable.) 


$Ji.25T%%.  Baltimore,  July  1,  1882. 

Fifteen  days  after  date,  without  grace,  I  promise  to  pay 
George  Brabburn,  or  bearer,  Four  Hundred  Twenty-five 
-ffy  Dollars,  value  received.  Silas  Weight. 

What  was  the  amount  due  on  this  note  at  maturity  ? 


332.    No.  6.— Notes  on  Demand  op  on  Time.    (Non-Negotiable.) 

$700'  Indianapolis,  May  31st,  1882. 

On  demand  after  date,  I  promise  to  pay  Robert  Carter, 
Seven  Hundred  Dollars,  with  interest  at  8%,  value  received. 

John  Hancock. 

Eequired  its  amount  at  sixty  days. 

7.  What  would  be  its  amount,  if  the  time  were  3  mo.  and 

the  rate  1%  ? 

Note. — Notes  of  the  above  form  are  not  assignable,  and  can  be  collected 
only  by  the  drawee. 


333.    No.  8.— Joint  Notes. 


S1600.  Sl,  LouiSj  Aug.  6>  i883. 

Two  months  after  date,  we  jointly  promise  to  pay  Horace 
Holben,  or  order,  Sixteen  Hundred  Dollars  negotiable  and 
'payable  without  defalcation  or  discount  with  6%  interest,  value 
received.  A.  H.  Stebbins, 

John  Wakd. 

Find  the  amount  due  at  maturity. 

Notes. — 1.  The  signers  of  a  "joint  note "  are  equally  responsible  for 
its  payment,  and  must  be  sued  jointly. 

2.  The  signers  of  a  "joint  and  several "  note  are  individually  responsi- 
ble for  the  whole  amount,  and  either  promisor  may  be  sued  alone. 


Commercial  Paper,  135 

334.    No.  9.— Notes  Payable  by  Installments. 


$8°°°'  Richmond,  Va.,  Oct.  16,  1883. 

For  value  received,  I  promise  to  pay  67.  C.  Davenport,  or 
order,  Two  Thousand  Dollars,  with  interest,  in  the  following 
manner,  viz :  Five  Hundred  Dollars  in  two  months  after  date, 
and  the  balance  in  installments  of  Five  Hundred  Dollars  every 
two  months  until  the  entire  amount  is  paid. 

G.  L.  Bennett. 

What  was  the  amount  of  each  payment,  at  6%,  without 
grace? 

10.  What  would  be  the  interest  and  amount  of  the  same 

note  at  7^?    At  5%? 

335.   No.  N.— Sight  Drafts. 


$3000.  New  Orleans,  Oct.  3d,  1883. 

At  sight,  pay  to  the  order  of  J.  B.  Hamilton  &  Co.,  Three 
Thousand  Dollars,  value  received,  and  charge  the  same  to 

J.  C.  Saunders. 

To  T.  J.  Sawyer,  Boston,  Mass. 

Note. — Drafts  are  drawn  payable  to  the  order  of  a  person  named  in 
them,  and  are  therefore  not  to  be  paid  until  indorsed  by  him. 

336.    No.  12.— Time  Drafts. 


$3560-  Grinnell.  Iowa,  Dec.  22,  1883. 

Ninety  days  after  date  pay  to  the  order  of  Calvin  Selden, 
Thirty-five  Hundred  Sixty  Dollars,  and  charge  the  same  to  the 
account  of  Sam'l  Barrett  &  Co. 

To  S.  Ball  &  Co.,  Trenton,  N.  J. 

Notes. — 1.  If  a  draft  is  payable  at  a  specified  time  after  sight,  the  date 
of  acceptance  and  the  time  of  the  draft  determine  its  maturity. 

2.  The  laws  of  N.  Y.  do  not  allow  "  grace  "  on  sight  drafts,  nor  on  time 
drafts  if  drawn  on  a  bank  or  banker. 


136  Percentage. 

337.  Find  the  date  of  maturity,  discount,  and  proceeds  of 
the  following  note,  offered  for  discount  June  10th,  at  6%. 

$750'  New  York,  May  8th,  1882. 

13.  Sixty  days  after  date,  I  promise  to  pay  George  E. 
Fisher,  or  order,  Seven  Hundred  Fifty  Dollars,  value  received. 

Seth  Low. 

Solution. — Sixty  days  from  May  8th  is  July  7th,  and  3  days  grace 
make  July  10th.  The  above  note  was  offered  for  discount  June  10th ; 
hence,  the  term  of  discount  was  30  days. 

Int.  at  6%  for  30  d.  on  $750  =      $3.75    Discount. 

$750 -$3.75  =  $746.25    Net  proceeds. 

Proof.  $750.00 

Date  of  maturity  July  10th. 


14.  A  note  of  $475,  dated  June  20,  1882,  payable  in  3  months 
after  date,  was  offered  for  discount  Aug.  11th  ;  what  were  the 
net  proceeds  at  6%  ? 

Find  the  date  of  maturity,  the  discount,  and  proceeds  of  the 
following  notes : 

$n6S-  Newark,  N.  J.,  Dec.  1st,  1882. 

15.  Four  months  after  date,  I  promise  to  pay  to  the  order  of 
Claflin  &  Co.,  Eleven  Hundred  Sixty-three  Dollars,  without 
defalcation  or  discount,  value  received.  James  Edsok. 

The  above  note  was  discounted  Feb.  15,  1883,  at  6%;  what 
were  the  proceeds  ? 


$2500. 


Knoxville,  Tenn.,  Apr.  12th,  1882. 


16.  Ninety  days  after  date,  ice  promise  to  pay  to  the  order  of 
Wm.  Day,  Twenty-Jive  Hundred  Dollars,  value  received. 

Monroe,  Lockwood  &  Co. 

The  above  was  discounted  May  15th,  at  6%  ;  what  were  the 
proceeds  ? 


Averaging  Accounts.  137 

AVERAGING    ACCOUNTS. 

338.  An  Account  is  a  record  of  business  transactions. 

339.  The  Average  of  several  unequal  numbers  is  their  sum 
divided  by  their  number.  Thus  the  average  of  H,  $6,  and  $8, 
is  $18-5-3  =  $6. 

340.  A  Day  Book  is  a  journal  of  accounts  in  which  are 
recorded  the  debts  and  credits  of  the  day. 

341.  A  Debtor  is  a  party  who  owes  another. 

342.  A  Creditor  is  a  party  to  whom  a  debt  is  due. 

343.  A  Ledger  is  a  book  to  which  a  summary  of  the 
accounts  of  the  "  Day  Book"  is  transferred  for  reference  and 
preservation. 

344.  The  Debits  or  Debts  are  placed  on  the  left,  marked  Dr. ; 
the  Credits  or  Payments  on  the  right,  marked  Cr. 

345.  An  Account  Current  is  a  running  account  containing 
a  record  of  the  mercantile  transactions  between  two  parties, 
showing  the  cash  balance  due  at  a  certain  date.  The  items 
usually  draw  interest  from  their  date,  or  some  specified  term  of 
credit,  to  the  time  of  settlement. 

Notes. — 1.  It  is  customary  for  merchants,  bankers,  and  brokers,  to 
render  their  accounts  at  stated  times,  as  monthly,  quarterly,  semi-annually, 
or  annually. 

2.  Whether  the  items  draw  interest  depends  on  custom  or  agreement 
between  the  parties.  Among  wholesale  merchants  and  jobbers,  it  is  cus- 
tomary to  charge  interest  on  accounts  after  six  months. 

3.  Among  retail  dealers,  mechanics,  farmers,  etc.,  the  items  seldom 
bear  interest ;  hence,  in  settling  such  accounts,  it  is  only  necessary  to  find 
the  merchandise  balance. 

346.  The  Commercial  or  Merchandise  Balance  is  the  differ- 
ence between  the  debit  and  credit  sides  of  an  account. 


138  Percentage. 

347.  The  Cash  Balance  is  the  sum  required  to  settle  an 
account  at  any  given  date. 

348.  The  Average  of  an  Account  is  the  equitable  time  when 
the  payment  of  several  debts  due  at  different  times  may  be 
made  at  one  time  without  loss  of  interest  to  debtor  or 
creditor. 

349.  The  Average  Time  is  called  the  mean  or  equated  time, 
and  the  process  by  which  it  is  found  is  often  called  Equation 
of  Payments. 

350.  The  Term  of  Credit  is  the  time  between  the  contrac- 
tion of  a  debt  and  its  maturity.     (Arts.  157,  313.) 

351.  The  Average  Term  of  Credit  is  the  time  at  which 
debts  due  at  different  times  may  be  equitably  paid. 

352.  Averaging  Accounts  depends  upon  the  following: 

Principles. 

1°.   The  rate  and  time  remaining  the  same, 
Double  the  principal  produces  twice  the  interest. 
Half  the  principal  produces  half  the  interest,  etc. 

2°.  The  rate  and  principal  remaining  the  same, 
Double  the  time  produces  twice  the  interest. 
Half  the  time  produces  half  the  interest,  etc.     Hence, 

3°.  Tlie  interest  of  any  given  principal  for  1  year,  1  month, 
or  1  day,  is  the  same  as  the  interest  of  1  dollar  for  as  many  years, 
months,  or  days,  as  there  are  dollars  in  the  given  principal. 

353.  To  find  the  Average  Time,  when  the  items  are  all  debits 
or  ail  credits. 

l.  A  bought  a  farm  July  15th  and  was  to  pay  $500  down, 
$300  in  2  months,  $400  in  6  months,  and  $600  in  8  months  ; 
what  is  the  average  term  of  credit  and  date  when  all  these 
payments  may  be  equitably  made  at  once  ? 


Averaging  Accounts,  139 

By  the  Interest  Method. 

Interest  of  $500  cash,  for  0  mo.,  at  6%  =  $0.00 
Interest  of  $300  for  2  mo.,  at  6%  =    3.00 

Interest  of  $400  for  6  mo.,  at  6%  =  12.00 

Interest  of  $600  for  8  mo.,  at  6%  =  24.00 

Ami  of  pay'ts  =  $1800  Int.  =  $39.00 

Taking  the  date  of  the  transaction,  viz.,  July  15th,  as  the  time  for  pay- 
ing all  the  items,  the  debtor  would  lose  the  int.  of  $300  for  2  mo.,  $400 
for  6  mo. ,  and  $600  for  8  months.  Therefore,  the  sura  of  items  ($1800)  is 
entitled  to  a  term  of  credit  equal  to  the  time  required  for  $1800,  at  6%, 
to  gain  $39.  Now,  the  interest  of  $1800  for  1  mo.  =  $9;  and  $39-i-$9 
=  4^  mo.,  term  of  credit ;  and  July  15th  +  4|  mo.  as  Nov.  25th, 
date  of  payment. 

By  the   Product  Method. 

The  first  payment  being  cash  has  no  solution. 

product.     The  next  payment  was  due  in  Items.    Time.       Product. 

2  mo.  and  its  interest  for  2  mo.  equals  the  500   X  0  =       00  mo. 
interest  of   $1   for  600  months.     (Prin.  300  X  2  =     600  mo. 

1°-)  400  x  6  =  2400  mo. 

The  interest  of  $400  for  6  mo.  equals  ^q^        q         4800  mo 

the  int.  of  $1  for  2400  mo. ,  and  the  int.         ~~ 

of  $600  for  8  mo.  equals  the  int.  of  $1  for         1800  )   7800 

4800  months.     Therefore  the  amount  of  ^Y^  ^jmg    4.1  mo. 

interest  due  on  the  sum  of  items,  equals 

the  int.  of  $1  for  7800  months,  and  $1800  is  entitled  to  a  term  of  credit 
equal  to  TJ7_  0f  7800  months,  or  4}  months. 

July  15  +  4$  mo.  as  Nov.  25th,  the  date  of  payment. 

Note. — This  method  is  the  same  in  principle  as  the  interest  method. 

2.  Bought  a  bill  of  goods  Apr.  20th  amounting  to  $6000,  on 
the  following  terms :  £  cash,  -J-  in  4  mo.,  and  the  balance  in 
6  mo. ;  at  what  date  may  the  whole  be  justly  paid  ? 

Am.  Av.  time  3£  mo.,  or  Aug.  5th. 

3.  On  a  certain  day  A  bought  a  horse  for  $175  on  30  d., 

3  cows  for  $120  on  45  d.,  80  sheep  for  $250  on  60  d.,  and  5  tons 
of  hay  for  $130  on  90  days;  what  is  the  average  term  of 
credit  ? 

4.  Bought  a  ship  for  $30000 ;  the  payments  were  $5000  cash, 
$8000  in  4  mo.,  $7500  in  6  mo.,  $4500  in  8  mo.,  and  the  bal- 
ance in  a  year  ;  what  is  the  average  term  of  credit  ? 


140  Percentage. 

354.  To  find  the  Average  Time  when  the  items  have  different 
dates  and  different  terms  of  credit. 

5.  .Required  the  average  date  at  which  the  following  items 
may  be  paid  at  once  without  loss  of  interest  to  either  party  : 

April  10,  merchandise  on  30  days,  $40. 

May      1,  "  40     "      $54. 

June  15,  "  30     u      $70. 

"      30,  "  40     "      $80. 

I.     By  the  Interest  Method. 

Due.  Time.     Items.  Int.  at  6#. 

May    10  (from  May  1st)  9  d.,  $40  =        $0.06 
June    10  «  40  d.,  $54  =  0.36 

July    15  "  75  d.,  $70  =  0.875 

Aug.      9  "  100d.,_$80=  1.333 

Int.  at  6%  for  1  day  of  $244  =.04  )  2.628 

65.7,or  66  d. 
Ans.  Date  of  pay't  is  66  d.  from  May  1st,  or  July  6th. 

Explanation. — The  earliest  date  at  which  any  item  matures  is  May 
10th ;  therefore,  taking  May  1st  as  the  standard  date,  and  finding  the 
interest  at  6  %  on  each  item  for  the  number  of  days  from  this  date  to  its 
maturity ;  the  sum  of  int.  =  $2,628,  the  sum  of  items  =  $244,  which  is 
entitled  to  a  term  of  credit  equal  to  the  time  required  for  it  to  gain  $2,628 
interest.  The  int.  of  $244  for  1  day,  at  6%  =  $0.04,  and  $2,628  -f-  .04 
=  65.7,  or  66  d.,  the  av.  time.     May  1st  +  66  d.  =  July  6th.     Hence,  the 

Eule. — Take  as  the  standard  the  first  of  the  month  in 
which  the  earliest  item  matures;  find  the  interest  on 
each  item-  from  the  standard  date  to  the  date  of  its  ma- 
turity, and  divide  the  sum  of  interests  by  the  interest  of 
the  sum  of  items  for  1  month  or  1  day,  as  the  case  may  be. 

The  quotient  will  be  the  number  of  months  or  days 
from  the  standard  date  to  the  average  date  of  payment. 
Add  this  number  to  the  standard  date  and  the  result 
will  be  the  equitable  date  of  payment. 

Notes. — 1.  If  the  earliest  due  date  is  the  standard,  its  item  has  no 
product,  but  it  must  be  included  in  the  sum  of  debts. 


Averaging  Accounts.  141 

2.  If  the  fraction  in  the  quotient  is  £  day  or  more,  1  day  is  added ;  if 
less  than  \  day  it  is  rejected. 

3.  In  computing  by  the  interest  method,  the  rate  forms  no  element  of 
the  calculation  ;  hence,  any  rate  may  be  used.  The  most  convenient  is 
6%  or  12%.  At  12%  the  int.  for  30  days,  or  1  mo.,  is  .01  ;  and  for  3  d., 
.001  of  the  principal,  or  \  as  many  thousandths  as  days. 

4.  Any  date  may  be  assumed  as  the  standard,  but  it  is  generally  more 
convenient  to  take  the  first  day  of  the  month  in  which  the  earliest  item 
falls  due,  or  the  last  day  of  the  preceding  month.  Some  prefer  the  earliest 
or  latest  date  of  any  item,  or  the  earliest  or  latest  maturity. 

II.    By  the  Product  Method. 

Assuming  May  1st  as  the  standard  date,  the  term  of  credit  for  the  first 
item  is  9  days. 

The  2d  item  due  June  10th,  the  time  from  May  1st,  is  40  days,  etc. 
Arranging  the  items  as  below  and  multiplying  each  by  the  number  of 
days  from  the  standard  date  to  its  maturity. 

Due.  Time.  Items.  Products. 

May  10,  9  d.  x  $40  =  360 
June  10,  40  d.  x  54  =  2160 
July  15,  75  d.  x  70  =  5250 
Aug.    9,  100  d.  x  _80     =  _8000 

Sum  of  items,  $244        )  15770  days. 
Av.  time,  64T^  d. 
May  1st +  65  days  =  July  5th,  date  of  pay't.     Hence,  the 

355.  Rule. — Find  the  date  when  each  item  matures. 
Take  the  first  day  of  the  month  in  which  the  earliest 
item  becomes  due  as  a  standard,  and  find  the  number  of 
days  from  this  to  the  maturity  of  each  of  the  other 
items. 

Multiply  each  item  by  its  number  of  days,  and  divide 
the  sum  of  the  products  by  the  sum  of  the  items.  Tlie 
quotient  will  be  the  average  term  of  credit. 

Add  the  average  time  to  the  standard  date,  and  the 
result  will  be  the  equitable  date  of  payment. 

Notes. — 1.  When  an  item  contains  cents,  if  less  than  50,  they  are 
rejected  ;  if  50  or  more,  $1  is  added. 

2.  In  averaging  accounts,  it  is  customary  to  consider  30  days  a  month. 
But  when  the  terms  of  credit  are  given  in  months,  calendar  months  are 
always  meant. 


142  Percentage, 

6.  A  grocer  sold  the  following  amount  of  goods :  June  3d, 
$380  on  90  days'  credit;  June  10th,  $485  on  30  d.;  July  21st, 
$834  on  70  d. ;  July  28th,  $573  on  40  d. ;  Aug.  2d,  $485  on 
40  d. ;  what  is  the  average  term  of  credit  and  date  of  payment  ? 

EXPLANATION. —  Due'         Time.       Items.         Products. 

The  second  item  is  due  Sept.     1,  G2  d.  X  $380  =  235G0 

July  10th.    This  being  July  10,     9  d.  x    485=    4365 

the    earliest    date  on  g     t  ^    gQ  ^  x    ^  =  mQQ 

S^SWS  S^    *  67  d.  x   573  =  38391 

for  the  standard  date.  Sept.  11,   72  d.  X_485  =  34920 

Finding   the    number  2757  )  176296 

of  days  from  this  date  

to    the    maturity     of  63.9  d. 

each  item  and  proceed-  July  1st  +  64  d.  =  Sept.  3d,  Date  of  Pay't. 
ing  as  in  Ex.  2d,  the 

average  time  is  64  days.  '  Date  of  pay't,  Sept.  3d. 

Note. — When  several  bills  are  bought  on  common  terms  of  credit, 
find  the  average  date  of  purchase,  and  add  to  the  result  the  common  term 
of  credit. 

7.  Sold  goods  as  follows  on  4  months  credit :  Aug.  20th, 
$975;  Sept.  4th,  $1150;  Sept.  16th,  $650;  Oct.  3d,  $846; 
Oct.  19th,  $578;  Nov.  19th,  $1240;  what  is  the  equitable  time 
of  payment  ? 

8.  Bought  the  following  bills  of  goods  on  4  months  credit : 
March  10th,  1879,  $250;  April  15th,  $260;  June  1st,  $540;  at 
what  time  is  the  amount  payable  ? 

9.  If  you  owe  a  man  $84  payable  in  4  mo.,  $120  in  6  mo., 
$280  in  3  months,  what  is  the  average  term  of  credit? 

10.  If  you  owe  one  bill  of  $175,  due  in  30  days  ;  another  of 
$812,  due  in  60  days;  another  of  $120,  due  in  65  days;  and 
another  of  $250,  due  in  90  days;  what  is  the  average  term  of 
credit  ? 

n.  Sold  goods  as  follows:  May  17th,  $560  on  30  d.;  June 
1st,  $435  on  45  d.;  July  7th,  $863  on  60  d.;  Aug.  13th,  $1000 
on  15  d. ;  what  is  the  equitable  time  of  payment  ? 

12.  Bought  March  5th,  a  carriage  on  6  mo.  for  $750 ;  March 
10th,  a  span  of  horses  for  $560  on  4  mo.;  April  1st,  a  set  of 
double  harness  $275  on  3  mo. ;  May  10th,  a  wagon  $160  on 
%  mo.;  what  is  the  average  term  of  credit  ? 


Averaging  Accounts.  143 

356.  To  find  the  Extension  of  Credit,  to  which  the  balance 
of  a  debt  is  entitled  when  partial  payments  have  been  made  before 
they  are  due. 

13.  A  sold  B  a  bill  of  goods  March  12th,  on  6  months, 
amounting  to  $1740 ;  July  10th,  B  paid  him  $500 ;  Aug.  6th, 
he  paid  $700  more  ;  to  what  additional  credit  is  B  entitled  on 
the  balance  ? 

Explanation.— March  12th +  6  operation. 

months  equals  Sept.  12th,  the  due  $500  X  64  =  32000 

date.      From   July   10th  to   Sept.  700  X  37  =  25900 

12th,  is  64  days.     From  Aug    6th  _~  }  — 

to  Sept.  12th,  is   37  days  ;    there-  L 

fore  the  int.  of  $500  =  int.  of  $1,  1740  107f  d. 

32000  days,  and  the  int.  of  $700  =     g     .    £^h      1Q7  d   =  p^  m^ 
int.  of  $1,  25900  days ;  both  pay-         r 
ments  equal  the  int.  of  $1,  for  57900  days. 

Therefore,  B  is  entitled  to  the  use  of  the  balance  ($1740—1200)  =  $540 
for  ^fa  of  57900  days,  or  107|  days  additional  time,  or  extension  of  credit 
on  the  balance.     The  equitable  date  of  payment  is  Dec.  28th.     Hence,  the 

Eule. — Multiply  each  -payment  by  the  time  from  its 
date  to  the  maturity  of  the  debt,  and  divide  the  sum  of 
the  products  by  the  balance  remaining  unpaid.  TJie 
quotient  will  be  the  equitable  extension  of  credit. 

Note. — If  a  partial  payment  is  made  before  a  debt  is  due,  equity 
requires  that  the  debtor  should  have  an  extension  of  credit  on  the  balance, 
equivalent  to  the  interest  of  the  pre-payment.  But  the  creditor  is  not 
always  willing  to  allow  this  and  is  not  required  to  do  it,  by  law. 

14.  A  man  bought  a  bill  of  goods  on  90  d.,  amounting  to 
$2340.75 ;  if  he  pays  $1000  down,  what  extension  ought  he  to 
have  on  the  balance  ? 

15.  A  man  owes  $1569.75,  payable  in  90  days ;  60  days 
before  it  is  due  he  pays  $350.86,  and  30  days  later  $211.89 
more ;  what  extension  ought  he  to  have  on  the  balance  ? 

Note. — In  finding  the  average  date  of  payment  some  accountants  omit 
the  cents  and  units  of  dollars,  using  only  the  nearest  number  of  tens  in 
the  multiplication.  Thus,  the  numbers  in  the  last  example  would  be 
$157,  $351,  and  $212.     This  shortens  the  process  materially. 


144 


Percentage. 


357.    To  find  the   Average   Time  when  an   account  has  both 
debits  and  credits. 

16.   What  is  the  average  time  and  date  of  paying  the  follow- 
ing account : 

Dr.  Geo.  Bancroft  in  acct.  with  Miller  &  Co.  Or. 


1883. 

1883. 

May   21 

For  Mdse.  3  mo. 

$500 

May  24 

By  Cash. 

$300 

"     28 

a          a                a 

250 

June   8 

"   Sundries  60  d. 

400 

June    9 

"       "     30  d. 

160 

July  21 

"   Cash. 

100 

Dr. 


Product  Method. 


Or. 


Due. 

Items. 

Days. 

Prod. 

Due. 

Items. 

Days. 

Prod. 

Aug.   21 

$500 

112 

56000 

May    24 

$300 

23 

6900 

"       28 

250 

119 

29750 

Aug.     7 

400 

98 

39200 

July      9 

160 

69 

11040 

July   21 

100 

81 

8100 

$910 
800 
110 


96790 
54200 


$800 


54200 


)  42590  (  387T*r  days,  or  390  d. 

Ans.  Bal.  $110,  due  in  390  d.  from  May  1st,  or  May  25th,  1884. 

Explanation. — Having  found  when  each  item  of  debt  and  credit 
becomes  due,  by  adding  its  term  of  credit  to  its  date,  we  assume  as  the 
standard  date  the  first  day  of  the  month  in  which  the  earliest  item  on  either 
side  of  the  account  matures,  viz.:  May  1st. 

Multiply  each  item  on  both  sides  by  the  number  of  days  between  its 
maturity  and  the  standard  date,  and  divide  the  difference  between  the 
sums  of  the  products  (42590),  by  the  difference  between  the  sums  of  the 
items  (110).     The  quotient  is  the  average  time  of  payment. 

Since  the  time  from  May  1,  1883,  to  May  1,  1884  =  1  year,  the  date  of 
payment  is  390  d.— 365  d.  =  25  d.  Hence  the  bal.  $110  is  equitably  due 
May  25th,  1884. 


Dr. 


Interest   Method. 


Cr. 


Due. 

Items. 

Time. 

Interest. 

Due. 

Items. 

Time. 

Aug.  21 

$500 

112  d. 

$9,331 

May  24 

$300 

23  d. 

"     28 

250 

119  d. 

4.95| 

Aug.   8 

400 

99  d.    ' 

July     9 

160 

69  d. 

1.84 

July  21 

100 

81  d. 

$910 
800 


$16.13 
9.10 


$800 


Int. 

$1.15 
6.60 
1.35 

$97lO 


Int.at6%on  $110  fori  d,  =  ,018)7.03  ( 390  days  from  May  1,  '83,  or  May  25, 


Averaging  Accounts.  145 

Explanation. — Taking  the  interest  at  6^,  there  is  a  bal.  due  at  the 
assumed  date,  May  1st,  '83,  of  $110,  and  a  loss  of  $7.08  interest.  To  bal- 
ance this  loss  of  int.,  the  payment  must  be  deferred  till  the  int.  of  $110  shall 
be  equal  to  $7.03.  The  int.  of  $110,  at  6%  for  1  d.,  is  .018,  and  $7.03-r- 
.018  =  390.  Hence,  the  time  of  payment  should  be  390  d.  =  1  yr.  25  d. 
from  May  1st,  '83  =  May  25th,  1884. 

358.  From  the  preceding  illustrations  we  derive  the  fol- 
lowing 

Rules. 

1.  Product  Method. —  Write  the  date  at  which  each 
item  on  both  sides  matures,  and  assume  the  first  day  of 
the  month  in  which  the  earliest  item  on  either  side 
becomes  due,  as  the  standard  date.  Find  the  number  of 
days  from  this  standard  to  the  maturity  of  the  respec- 
tive items. 

Multiply  each  item  by  its  number  of  days,  and 
divide  the  difference  between  the  sums  of  products  by 
the  difference  between  the  sums  of  items ;  the  quotient 
will  be  the  average  time. 

If  the  greater  sum  of  items  and  the  greater  sum 
of  products  are  both  on  the  same  side,  add  the  average 
time  to  the  assumed  date ;  if  on  opposite  sides,  subtract 
it ;  and  the  result  will  be  the  date  when  the  balance  of 
the  account  is  equitably  due. 

Notes. — 1.  In  finding  the  maturity  of  notes  and  drafts,  3  days  grace 
should  be  added  to  the  specified  time  of  payment. 

2.  When  no  time  of  credit  is  mentioned,  the  transaction  is  understood 
to  be  for  cash,  and  the  payment  due  at  once. 

II.  Interest  Method.— Find  the  interest  of  each  item 
for  the  time  from  the. standard  date  to  the  maturity  of 
the  respective  items,  and  divide  the  balance  of  the 
interests  by  the  interest  of  the  balance  of  items  for  1  day 
or  1  month ;  the  quotient  will  be  the  number  of  days  or 
months,  as  the  case  may  be,  between  the  standard  date 
and  the  time  of  settlement. 

When  the  balance  of  account  and  interest  are  both,  on 
the  same  side,  add  this  to  the  standard  date ;  if  on  oppo- 
10 


146 


Percentage, 


site  sides,  subtract  it ;  the  result  will  be  the  date  of  set- 
tlement. 

Note. — The  average  time  will  be  the   same   whatever  the  rate  of 
interest. 


359.  It  is  advisable  for  the  learner  to  solve  the  following 
examples  by  both  the  preceding  methods : 

17.  Balance  the  following  account  by  both  methods. 
Dr.    J.  H.  Strong  &  Co.  in  acct.  with  Smith  &  Crane.     Cr. 


1883. 

Mar.  25 

To  Mdse.,  60  d. 

$560 

Apr.  30 

By  Sundries,  30  d. 

$450 

Apr.     7 

a         ((              a 

830 

July  13 

"  Cash. 

500 

May     2 

a         a              {( 

730 

Aug.  31 

"  Dft.,  30  d. 

260 

Note. — In  this  example  the  bal.  of  items  and  excess  of  products  being 
on  opposite  sides,  the  average  time  is  subtracted  from  the  standard  date. 


18.  What    is  the   balance   of    the    following    account   and 
when  due  ? 

Dr.         H.  Morgan  in  acct.  with  Lockwood  &  Co.         Cr. 


1880. 

1880. 

July  20 

To  Sundries. 

$760 

Aug.  26 

By  Flour. 

$520 

Aug.  10 

a        (( 

540 

Sept.  12 

"  Stocks,  30  d< 

300 

Sept.  15 

a            a 

850 

Oct.      1 

"  Cash. 

385 

19.  Find  the  average  time  of  paying  the  following  account : 
Dr.  George  Jenkins.  Vrs 


1881. 

1881. 

Mar.     1 

To  Mdse,,  30  d. 

$500 

Apr.  12 

By  Draft,  20  d. 

$400 

Apr.     5 

"       <<       3  mo. 

700 

May  10 

"  Cash. 

540. 

May  20 

"       "       4  mo. 

850 

June    4 

a,      a 

60O 

Averaging  Accounts.  147 

20.  What  is  the  balance  of  the  following  acct.  and  when  due  ? 

Dr.  Wm.  H.  Jackson.  Or. 


June    1 

To  bal.  of  acct. 

$745.37 

June  10 

By  grain,  30  d. 

$545.60 

"     20 

"  silks,  30  d. 

1050.83 

July  12 

a       ((        tt 

675.31 

July  14 

"  wh.  g'ds," 

971.55 

"    31 

"  cash. 

900.40 

Aug.    3 

"  sundries," 

1260.10 

Aug.  15 

"  note,  30  d. 

1000.00 

21.  At  what  date  can  the  balance  of  the  following  account  be 
equitably  paid  ? 


D 


W.  H.  Hendeickson. 


Or. 


1882. 

1882. 

Apr.     7 

To  Mdse.,  2  mo. 

$300 

May     1 

To  Mdse.,  60  d. 

$350 

July    5 

"       "       3  mo. 

500 

June  10 

"       M      30  d. 

500 

Aug.  10 

"       "I  mo. 

400 

Aug.  30 

"  Cash. 

250 

360.  In   the  following  examples    different  dates  may.be 
assumed -as  the  standard. 


22.  What  is  the  balance  of  the  following  account  and  when 
equitably  due  ? 


Dr. 


A.  P.  Holmes  in  acct.  with  Lord  &  Taylor. 


Or. 


1878. 

1878. 

Aug.  14 

To  Sundries. 

$1100 

July     5 

By  Mdse. 

$585 

"     21 

a             (( 

950 

"     18 

a         a 

640 

Sept.    1 

a              a 

760 

Aug.  11 

a         <( 

965 

*     10 

<(                 (4 

1000 

Sept.  20 

a         a 

800 

Am.  Bal,  $820,  Due  Oct,  28,  1878, 


148  Percentage. 

23.  Find  the  balance  of  the  following  acct.  and  when  due : 
Dr.  A.  B.  in  acct.  with  0.  D.  Cr. 


1880. 

1880. 

Aug.  11 

For  Mdse. 

$160 

Sept.    2 

By  Sundries. 

$75 

Sept.    5 

a           u 

240 

Oct.    10 

"  Note,  30  d. 

100 

Oct.   20 

((  1  horse. 

175 

Nov.    1 

"  Cash. 

110 

24.  Find  the  bal.  of  the  following  acct.  and  when  due : 
Dr.  Wm.  Gorham  in  acct.  with  John-  Hendrix.  Cr. 


1880. 

1880. 

Feb.  10 

For  Mdse.,  4  mo. 

$450 

Mar.  20 

By  Sundries,  3  m. 

$325 

May  11 

<.(            a        o       (t 

500 

July     9 

"  Draft,  60  d. 

150 

July  26 

a            a       o      li 

360 

Sept.  15 

"  Cash. 

400 

25.  Average  the  following  account : 
Dr.  James  Green  &  Co. 


Or. 


1882. 

1882. 

Jan.   10 

To  Mdse.,  3  mo. 

$450 

!jan.     1 

By  Bal.  of  Acct. 

$485 

"     25 

"       "       30  d. 

265 

Feb.  10 

"  Note,  3  mo. 

2500 

Apr.  20 

«       "       3  mo. 

850 

Mar.     1 

1 

u  Draft,  30  d. 

360 

\I   26.  Balance  the  following  account : 
*  Dr.  C.  J.  Hamilton. 


Cr. 


1880. 

1880. 

Jan.   20 

To  Sundries,  30  d. 

$500 

Jan.   20 

Byrealestate,60d. 

$400 

Feb.   12 

60  d. 

340 

Mar.     1 

"  Draft,  60  d. 

200 

Mar.     1 

30  d. 

300 

: 

"     20 

"Cash. 

400 

Cash  Balance. 


149 


27.  Average  the  following  account ; 
Dr.  Henry  J.  Raymond  &  Co. 


Or. 


1882. 

1882. 

Aug.  10 

To  Mdse.,  60  d. 

$150 

Aug.  25 

By  Mdse.,  30  d. 

1500 

Oct     1 

"  Cash. 

350 

Sept.  20 

"       "       30  d. 

350 

"     18 

"  Dft.,  30  d. 

250 

28.  Find  when  the  balance  of  the  following  account  becomes 
due: 

A.  B.  bought  of  C.  D.,  July  16th,  1883,  merchandise  $350  ; 
Aug.  11th,  $465;  Sept.  9th,  $570;  Sept.  14th,  $850;  Oct.  18th, 
$780.  The  former  paid  August  1st,  $360;  Sept.  30th,  in  grain 
$340;  Oct.  5th,  cash  $500;  Oct.  21st,  $625. 

Cash     Balance. 
361.    To  find  the  Cash  Balance  of  an  account,  at  a  given  date. 

29.  Find  the  cash  balance  of  the  following  acct.,  due  July 
15th,  1880,  at  6%  int. : 

Dr.     Thomas  Packard  in  acct.  with  Henry  Selden.     Cr. 


1880. 

Mar.  10 

To  Mdse.,  30  d. 

$650 

1880. 

Apr.  20 

By  Bal.  acct. 

$500 

Apr.     1 

"  Cash. 

1000 

May  13 

"  Dft.  on  90  d. 

940 

May  26 

"  Note,  60  d. 

1260 

June    1 

"  Bank  Stock. 

1000 

OPERATION. 


Date. 

1880. 

Apr.    9 

"      1 
July  28 


Days. 

Items. 

Products. 

Date. 
1880. 

Days. 

Items. 

97 

$650 

63050 

Apr.  20 

86 

$500 

105 

1000 

105000 

Aug.  14 

-30 

940f 

-13 

1260* 

June   1 

44 

1000 

2910         28200f  2440 

2440       196250 

Bal.  of  items,     $470       103380 

6 1 000  )  92J870    Balance  of  products. 
Bal.  of  int.,     $15,478 
And  $470 +  $15.48  =  $485.48,  Cash  balance. 


Products. 
43000 

44000 
16380* 
103380 


150  Percentage. 

Analysts. — Taking  the  given  date  of  settlement,  July  15th,  as  the 
standard,  we  find  the  maturity  of  each  item,  as  before,  in  days.  The 
third  item  of  debits  is  a  note  on  60  d.,  with  3  days  grace ;  hence,  it  is  not 
due  till  13  days  after  the  settlement,  or  July  28th.  This  is  indicated  by 
the  sign  — ,  and  the  item  being  entitled  to  interest  for  13  days,  its 
product  is  placed  on  the  credit  side  of  the  account. 

The  second  item  of  credits  is  a  draft  on  90  days,  with  3  days  grace,  and 
it  is  not  due  till  Aug.  14th,  30  days  after  settlement,  which  is  also 
indicated  by  the  sign  — ,  and  its  product  is  placed  on  the  Dr.  side. 

Since  each  item  is  multiplied  by  its  number  of  days,  dividing  the 
balance  of  products  by  6000  gives  $15.48  =  interest  of  bal.  at  6%.  And 
the  bal.  of  items,  $470  +  $15. 48  =  $485.48,  the  cash  balance  required. 
Hence,  the 

Rule  for  Product  Method. 

Find  the  number  of  days  from  the  given  date  to  the 
maturity  of  eaeh  item. 

Multiply  each  item  on  both  sides  by  its  number  of 
days ;  if  the  maturity  of  any  debit  item  extends  beyond 
the  date  of  settlement,  place  its  product  on  the  credit 
side ;  if  the  extension  is  a  credit,  place  its  product  on  the 
debit  side. 

Divide  the  balance  of  products  by  6000,  and  the  quo- 
tient will  be  the  balance  of  interest  at  6%. 

J¥7ien  the  balance  of  items  is  on  the  same  side  with 
the  balance  of  interest,  add  the  interest  to  the  items ; 
if  on  opposite  sides,  subtract  it;  the  result  will  be  the 
cash  balance  required. 

Notes. — 1.  In  settling  mercantile  accounts  interest  is  not  always 
reckoned.  This  matter  is  regulated  by.  previous  agreement.  When 
interest  is  charged  it  is  calculated  from  the  time  the  account  is  due.  It 
may  first  be  found  at  12%  as  in  averaging  accounts,  and  the  result 
changed  to  the  legal  rate. 

2.  The  reason  for  placing  the  product  of  an  item  on  its  own  side 
when  it  becomes  due  before  the  time  of  settlement,  is  because  it  is 
entitled  to  interest  for  the  intervening  time. 

In  like  manner,  if  a  credit  extends  beyond  the  settlement,  equity 
requires  that  interest  should  be  allowed  on  that  item.  Hence,  its 
interest  for  that  time  must  either  be  subtracted  from  its  own  side,  or  be 
added  to  the  opposite.  The  latter  is  the  more  convenient,  and  therefore 
adopted. 


Cash  Balance. 


151 


362.  The  amount  due  on  an  account  current  at  a  given  date 
may  be  found  by  the  interest  method,  or  by  the  product 
method.  When  interest  is  not  charged  it  is  only  necessary  to 
find  the  merchandise  balance.     (Art.  346.) 

30.  What  is  the  cash  balance  on  the  following  account,  July 
1st,  1881,  interest  at  6%  ? 


Dr. 


A.  B.  in  account  with  C.  D. 


Or. 


1881. 

!        1881. 

March  1 

For  Mdse. 

$120 

!April   2 

By  Sundries. 

$300 

May    10 

a        a 

340 

"     20 

"   Cash. 

450 

May    22 

"      "    on30d. 

560 

June     8 

"   dft.  on  30  d. 

120 

Interest  Method. 


Items. 

Days. 

Int. 

Due. 

1881. 

Items. 

Days. 

Int. 

$120 

122 

$2.44 

April    2 

$300 

90 

$4.50 

340 

52 

2.95 

"     20 

450 

72 

5.40 

560 

10 

0.93 

July   11 

120* 

-10 

1020 

0.20* 

870 

$9.90 

870 

6.52 

6.52 

$150- 

$3.38  = 

$146.62  ca 

ish  balance. 

Ba 

1.  of  Int. 

,  $3.38 

Due. 

1881. 

March  1 

May    10 
June  21 


Kule  for  Interest  Method. — Take  the  given  date  of 
settlement  as  the  standard  and  multiply  the  respective 
items  by  the  number  of  days  between  this  date  and  the 
due  date  of  each  item. 

Find  the  interest  on  each  item  at  the  given  rate,  and 
the  difference  between  the  sums  of  debit  and  credit 
interest  will  be  the  balance  of  interest. 

WTien  the  balance  of  items  and  the  balance  of  interest 
are  both  on  the  same  side,  add  them,  when  on  opposite 
sides,  subtract  them,  the  result  will  be  the  cash  balance. 

Note. — Interest  tables  are  much  used  in  making  out  accounts  current. 
After  an  account  is  balanced  it  is  considered  the  same  as  cash  and  draws 
interest  on  the  amount. 


152  Percentage. 

363.  Second  Form  of  an  account  current  including  interest. 
Br.  A.  B.  in  %  current  with  0.  D.  Cr. 


1881. 

Days.  Int. 

Items. ! 

1881. 

Days. 

Int. 

Items. 

March  1 

Mdse. 

122    2.44 

$120.00 

April  2  Sundries. 

90 

4.50 

$300 

May  10 

(i 

52    2.95 

340.001 

■     20  Cash. 

72 

5.40 

450 

May  22 

"    as  June  21 

10  I0.93 

560.00 

July  11  Dft.  on  30  d. 

-10 

120* 

July    1 

Int.  on  dft. 

10    0.20* 

July    1  Bal.  of  Int. 

3.38 

U         u 

Bal.  of  Int. 

3.38 

11 

"     M  Acct. 

146.62 

Balance. 

9.90 

1020.00 

1 

9.90 

1020.00 

ii         ii 

$146.62 

Note. — Since  the  date  when  the  draft  is  due,  is  10  days  beyond  the  time 
of  settlement,  interest  is  charged  for  that  time  to  the  Dr.  side.  As  the 
balance  of  interest  is  on  the  Cr.  side,  the  draft  is  credited  to  items  on  that 
side  and  charged  to  interest  on  the  other. 

31.  Find  the  cash  balance  of  the  following  %,  Aug.  5th, 
1882,  at 

Dr. 


\o/? 


Geo.  Bancroft  in  %  with  H.  Greely. 


Cr. 


1882. 

June  10 

To  Mdse. 

$200 

1882. 

June  15 

By  Cash. 

$100 

*    30 

a      a 

300 

"     30 

a         a 

150 

July  11 

a      a 

120 

July     6 

a         a 

200 

"    24 

a         a 

250 

"     30 

a         a 

300 

32.  Find  the  cash  balance  of  the  following 


i,  Oct.  30,  1882, 


at 


Dr. 

James  Morris  in 

%  with  John  Jay. 

Cr. 

1882. 

Jan.     5 

To  Mdse.,  60  d. 

$182 

1882. 

Feb.     1 

By  bal.  of  %. 

$300 

Feb.   12 

u       "      30  d. 

270 

Mar.  30 

"  Cash. 

250 

Mar.     7 

"       "      30  d. 

480 

Apr.  20 

a        a 

200 

Apr.  15 

"       "      60  d. 

640 

June  15 

"  Note,  30  d. 

300 

May     9 

"       "      60  d. 

530 

Aug.    1 

"  Cash. 

400 

33.  Find  the  cash  balance  of  the  same  account  at 


Averaging  Accounts  Current 


153 


34.  What  is  trie  cash  balance  of  the  following  acct.,  Dec.  31st, 
1809,  at  Y/o  ? 
Dr.        S.  Parkhurst  in  acct.  with  G.  P.  Putnam.         Or. 


1869.       ! 

Sept.  10  To  Mds.,  30  d. 

$1250.15 

1869. 

Sept.  25 

By  Mds.,  60  d. 

$1560.50 

Oct.     1 

"      "    60  d. 

1015.60 

Oct.    10 

"      "    90  d. 

948.30 

"    23 

"      "     45  d. 

1500.85 

"     30 

"      M    40  d. 

1430.65 

Nov.  15 

"      "     60  d. 

1743.44 

Dec.  15 

"      "    30  d. 

1365.42 

35.  What  is  the  cash  balance  on  the  following  acct.,  Jan. 
10th,  1882  ? 

Dr.     S.  B.  Chittenden  in  acct.  with  A.  T.  Stewart.     Or. 


1881. 

Aug.    4 

To  Sundries,3  m. 

$1400 

July     5 

By  Mdse.,  3  mo. 

$685 

*     20 

a            a            a 

1050 

"     18 

a         <(              tt 

840 

Sept.  10 

a            a            a 

780 

Aug.  11 

a         ((              a 

960 

"    24 

a            a            tt 

1300 

"     18 

"  Draft,  30  d. 

800 

36.  Reduce  the  following  transactions  to  the  form  of  an 
acct.  bearing  interest  at  6%,  and  find  the  cash  balance  : 

Feb.  lith,  1870,  C  bought  goods  of  D  amounting  to  $1250; 
March  14th,  a  bill  of  $2160 ;  Apr.  10th,  a  bill  of  $1700;  Apr. 
30th,  a  bill  of  $1070 ;  May  6th,  a  bill  of  $2000.  March  1st, 
1870,  0  sold  a  bill  to  D  of  $1640  ;  March  20th,  a  bill  of  $1160; 
Apr.  15th,  a  bill  of  $1600  ;  May  1st,  a  bill  of  $1340 ;  May  21st, 
a  bill  of  $1000 ;  what  was  the  cash  balance  June  10th,  1870  ? 

37.  What  was  the  cash  balance  due  July  20th,  1869,  on  the 
following  account,  at  1%  int.  ? 

s(Dr.  George  Clark  &  Co.  in  acct.  with  Chas.  Anderson.  Cr. 


1869. 

Mar.     1 

For  Mdse.,  3  mo. 

$500 

1869. 

Apr.     5 

By  Mdse.,  3  mo. 

$350 

"     20 

"      2  mo. 

750 

"    20 

"       "       2  mo. 

900 

Apr.  10 

"      5  mo. 

410 

May     1 

"       "       4  mo. 

620 

May  21 

"       1  mo. 

600 

"    22 

"  Cash. 

200 

1 54  Percentage. 

38.  Find  the  balance  due  Sept.  1st,  at  6%  on  the  preceding 
amount. 

39.  Find  the  balance  of  the  same  account  due  Nov.  1st, 
at  6%. 

40.  Reduce  the  following  memoranda  to  the  form  of  an 
account,  and  find  the  cash  balance  due  Jan.  1st,  1879  : 

Aug.  1st,  1878,  A  bought  goods  of  B  amounting  to  $560 ; 
Aug.  26th,  $840 ;  Sept.  21st,  $1000 ;  Oct.  12th,  $1370 ;  and 
Nov.  1st,  $600.  A  sold  B,  Sept.  11th,  1878,  wheat  amounting 
to  $350 ;  Oct.  1st,  wool  amounting  to  $760 ;  Oct.  31st,  $400 
worth  of  butter  ;  and  Nov.  16th,  paid  him  $1000  cash. 


Account    Sales. 

364.  An  Account  Sales  is  a  record  of  the  goods  sold  by  an 
agent  for  his  principal,  with  his  expenses  and  charges. 

Notes. — 1.  The  charges  include  freight,  cartage,  storage,  advertising, 
insurance,  commission,  guaranty,  etc. 

2.  The  invoice  or  sales  form  the  credit  side  of  the  account,  and  the 
expenses  the  debit  side. 

l.  H.  Standart,  of  Detroit,  sold  March  12,  1883,  the 
following  consignment  of  goods  for  J.  L.  Starbuck  &  Co.,  of 
Boston : 

150  pieces  Merrimac  prints,  at  $4  ;  135  pieces  shirting,  at 
$7.50;  1  case  of  85  Bay  State  shawls,  at  $8.75  ;  65  pieces  flan- 
nel,  at  $12.50;    300  pair  shoes,  at  $2.25;    150  pair  boots, 

at  $4.20. 

Charges  for  freight,  $35.00  ;  cartage,  $3.50;  storage,  $5.00  ; 
insurance,  $6.50;  commission  and  guaranty,  b%.  What  were 
the  net  proceeds  ? 


Averaging  Accounts  Sales. 


155 


Account  Sales  of  Merchandise  for  acct.  and  risk  of 
J.  L.  Starbcjgk  &  Co.,  Boston. 


Mar.  12 


To  J.  Smith,  150  pes.  Mer.  pr.  @  $4 
"        135  pes.  Shirt.®  $7.50 

Hoyt  &  Co.,  1  c.  85  B.S.sh.@$8.75 
"  65  pes.  flan.  @  $12.50 

L.  Wood,  300  pr.  shoes  @  $2.25. 
"        150  pr.  boots  @  $4.20, 

Charges. 
Freight,      -------- 

Cartage,      -    - 

Storage,      --.----- 

Insurance,  -- - 

Commission  and  Guaranty,  5$,  - 
Net  Proceeds,    -    - 


$600 

1012 

50 

743 

75 

812 

50 

675 

630 

$4473 

$35 

3 

50 

5 

6 

50 

223 

69 

273 

$4200 

75 


69 
06 


2.  Put  the  following  into  the  form  of  an  Account  Sales : 

James  Scott,  of  New  Orleans,  sold  on  account  of  J.  Hamil- 
ton, of  Cincinnati,  Nov.  16th,  1882,  300  bbls.  of  pork  to 
W.  Gerard  &  Co.,  at  $27 ;  1150  hams,  at  $1.75,  to  J.  Ramsey ; 
875  kegs  of  lard,  each  containing  56  lb.,  at  12  cts.,  to  Henry 
Parker,  and  750  lb.  of  cheese,  at  18  cts.,  to  Thomas  Young. 

Nov.  30th,  1882,  paid  freight,  $65.30;  cartage,  $15.25; 
insurance,  $6.45;  commission  and  guaranty,  at  5%.  What 
were  the  net  proceeds  ? 

3.  Samuel  Basset,  of  New  York,  sold  on  account  of  James 
Field,  of  St.  Louis,  Dec.  3d,  1882,  85  bales  cotton,  at  $96.50; 
63  barrels  of  sugar,  at  $48.25 ;  37  bbls.  molasses,  at  $35. 

Paid  freight,  $45.50  ;  insurance,  $15;  storage,  $35.50;  com- 
mission and  guaranty,  3 \%.     What  were  the  net  proceeds  ? 

365.  The  Commission  and  other  charges  are  considered  due 
by  some  at  the  average  date  of  sales ;  by  others  at  the  average 
maturity  of  sales.    This  is  usually  settled  by  agreement. 


156 


Percentage. 


Note. — The  method  of  averaging  an  account  sales  is  the  same  as  that 
for  averaging  an  account  having  both  debits  and  credits,  except  in  the 
matter  of  adjusting  the  date  for  the  commission  and  other  charges. 

366.  To  Average  an  Account  Sales,  and  find  when  the  net  pro- 
ceeds are  due. 

4.  Average  the  following,  and  find  the  due  date  of  net 
proceeds: 

Eeceived  on  consignment,  1000  bbl.  flour  from  B.  &  Co., 
Chicago. 

Sales. 


July 

11 

Aug. 

5 

u 

20 

Sept. 

2 

July 

1 

u 

1 

a 

3 

200  bbls.  flour,  sold  on  30  d. 

350     "  "            "       10  d. 

250     "  "            *       30  d. 

200     "  "            "       60  d. 

Charges. 

Freight, -    - 

Cartage, 

Storage, - 

Commission,  2\%  on  $5920,     • 

Commercial  Balance,     - 


55.50 
6.20 
6.00 

5.75 


|$1100 

00 

2170 

00 

1500 

00 

1150 

00 

$5920 

$450 

25 

30 

75 

150 

00 

148 

00 

779 

$5141 

00 


00 
00 


SOLUTION. 


I.  Find  the  average  date  of  sales 


Date. 
Due     Aug.  10 

"     Sept.  19 
"     Nov.    1 


Items. 

$1100 
2170 
1500 
1150 

$5920 


Days. 
40 
45 
80 

123 


Products. 

$44000 

97650 

120000 

141450 

)  403100 


Av.  time  of  sales,  68  days. 
Sales  due  July  1st +  68  d.  =  Sept.  7th. 


Averaging  Accounts  Sales.  157 

II.  Find  the  average  date  of  Charges : 


Date. 

Items. 

Days. 

Products. 

ue    July  1 

$450.25 

0 

$00.00 

u               u           1 

30.75 

0 

00.00 

«      3 

150.00 

2 

300.00 

"      Sept.  7 

148.00 

68 

10064.00 

779.00 

)  10364.00 

A  v.  time,  13  days. 
Charges  due  July  1st  + 13  d.  =  July  14th. 

Averaging  the  sales  and  expenses,  they  now  stand  as  follows : 

Date.  Items.    Days.      Prod.  Date.         Items.     Days.      Prod. 

Due  July  14      $779      13      10127  |  Due  Sept.  7     $5920      68      402560 

_779  ^0127 

15141  )  392433 

Av.  time,  76  d. 
Net  proceeds  $5141  due  July  1st +  76  d.  =  Sept.  15.     Hence,  the 

Rule. — I.  Find  the  amount  and  the  average  date  of 
sales.  The  date  of  sales  will  be  the  date  of  the  commis- 
sion and  guaranty.     (Art.  357.) 

II.  Find  the  average  date  of  the  charges,  make  the 
charges  the  debits  and  the  sales  the  credits,  and  find  the 
average  date  for  paying  the  balance. 

5.  Put  the  following  items  into  the  form  of  an  account  sales, 
find  the  net  proceeds  and  date  of  payment : 

A.  B.  Harrison,  of  Buffalo,  sold  a  consignment  of  goods 
from  Chase  &  Co.,  Chicago,  as  follows:  Nov.  loth,  1882, 
135  chests  tea,  at  $45,  on  30  d. ;  'Nov.  20,  75  sacks  coffee,  at 
$28,  on  2  mo.;  Dec.  1,  256  kegs  lard,  at  $4.50,  30  d.;  same 
date  285  tubs  butter,  at  $18.37,  on  2  mo.  Paid  freight 
Dec.  1,  $23.75;  cartage,  $5.40;  storage,  Dec.  10,  $7.80; 
commission,  2J$. 

6.  Same  parties  sold  Sept.  1,  on  3  mo.,  3520  lb.  sugar,  at 
!12J;  Sept.  15th,  25  chests  tea,  each  85  lb.,  at  .98,  on  2  mo.; 
Oct.  2,  28  half-chests  Oolong  tea,  42  lb.  each,  at  $1.05,  on 
2  mo.  The  charges  were  paid  Oct.  15,  freight  and  cartage  $85, 
commission  and  guarantee  5%. 


1 


AET^ERSHIP. 


fe-11-^- 


367.  Partnership  is  the  association  of  two  or  more  persons 
for  the  transaction  of  business. 

368.  The  persons  thus  associated  are  called  Partners. 

369.  The  association  is  called  a  Firm,  Company,  or  House. 

370.  The  Capital  is  the  money  or  property  furnished  by  the 
Partners. 

371.  The  Assets  or  Resources  of  a  firm  are  various  kinds  of 
property  belonging  to  it. 

372.  The  Liabilities  are  its  debts. 

373.  The  Net  Capital  or  Worth  of  a  firm  is  the  excess  of  its 
property  above  its  liabilities. 

374.  The  Insolvency  of  a  firm  is  the  excess  of  its  liabilities 
above  its  property  or  resources. 

Note. — The  Net  Insolvency  is  the  difference,  made  by  the  gains  of  a 
firm,  between  its  present  and  former  insolvency. 

375.  The  Net  Gain  or  Loss  is  the  difference  between  the 
total  gains  and  total  losses. 

376.  Partnerships  are  General,  Special,  or  Limited. 

377.  A  General  Partnership  is  one  in  which  not  only  the 
property  of  the  firm,  but  the  private  property  of  each  of  the 
partners  is  liable  for  its  debts. 

378.  A  Special  Partnership  is  one  in  which  a  person  puts 
in  a  certain  amount  of  money,  and  loses  only  that  amount  in 
case  oifailure* 


Partnership.  159 

379.  A  Limited  Partnership  is  one  in  which,  if  certain 
things  are  done,  a  person's  private  property  shall  not  be  respon- 
sible for  the  firm  debts. 

Notes. — The  things  required  in  most  States  for  the  formation  of 
limited  partnerships  are :  -v 

1st.  The  arrangements  must  be  in  writing,  signed  and  recorded  in  a  cer- 
tain public  office. 

2d.  There  must  be  at  least  one  general  partner. 

3d.  The  special  partners  can  take  no  actim  part  in  the  business,  and 
their  names  must  not  appear  in  the  firm  name. 

4th.  The  amount  which  the  special  partners  contribute  must  be  actually 
paid  in  and  duly  advertised.  If  any  one  of  these  requirements  is  omitted* 
the  partnership  becomes  general. 

380.  The  gains  and  losses  of  a  firm  are  divided  according 
to  the  previous  agreement  between  the  partners.     Thus, 

In  some  cases  the  gains  or  losses  are  divided  in  proportion  to> 
the  capital,  or  the  average  investments  of  the  partners. 

In  others  the  inequalities  of  'their  investments  are  adjusted 
by  allowing  each  partner  a  specified  salary,  which  is  taken 
from  the  gains  of  the  firm  before  they  are  divided,  no  interest 
account  being  kept. 

But  the  more  common  practice  is  to  credit  each  partner  with 
interest  on  his  capital  and  charge  him  interest  for  sums  he 
draws  out ;  then  divide  the  gain  or  loss  according  to  certain 
percentages  or  fractional  parts. 

Notes.— 1.  Upon  dissolution  the  partners  are  individually  liable  for 
the  existing  debts  of  the  firm. 

2.  If  a  partner  assigns  his  interest  in  the  business,  the  word  "  release" 
must  be  used  in  order  to  pass  the  whole  interest. 

381.  To  find  the  Net  Gain  or  Loss  of  a  Partnership. 

l.  A  and  B  commenced  business  with  a  capital  of  $8000 
cash  and  $3000  merchandise,  and  bills  payable  $1450.  At  the 
end  of  the  year  they  had  $5500  in  banfc^$4500-  ij%  goods,  and 
$2950  in  bills  receivable,  and  debts  ow<£t  by  firm  $9$).  What 
was  the  net  gain  or  los§  of  the  firm  ? 


160  Percentage. 


Assets  at  Commencement. 

Cash $8000 

Mdse 3000 

Assets 11000 

Liabilities 1450 


Net  capital $9550 

$12000- $9550  =  $2450,  Net  gain,  Ans.     Hence,  the 


Assets  at  Close. 

Cash  in  bank $5500 

Mdse 4500 

Bills  receivable 2950 

Assets 12950 

Liabilities 950 

Net  capital $12000 


Rule. — To  find  the  Net  Gain. — Subtract  the  net  capital 
at  commencement  from  the  net  capital  at  closing. 

To  find  the  Net  Loss.— Subtract  the  net  capital  at  clos- 
ing from  the  net  capital  at  commencement. 

382.  To  divide  the  Gain  or  Loss  in  proportion  to  each  partner's 
capital,  when  employed  for  the  same  period. 

l.  A  and  B  formed  a  partnership ;  A  furnished  $3000, 
B  $5000  ;  they  gained  $2000,  and  agreed  to  share  the  profit  or 
loss  in  proportion  to  the  capital  of  each  ;  what  was  each 
partner's  share  ? 

1st  Method.— $3000  +  $5000  =  $8000    Capital  of  firm. 

f  $$=§»  hence  A's  share=$2000  x  f  =    $750    A's  gain. 
5ooo_5^      m      B's  share  =  $2000  x  §  =  $1250    B's  gain. 

Proof.— Whole  gain  =  $2000 

2d  Method.— The  gain  $2000-=-$8000  (cap.)=.25,  or  25%.    (Art.  216.) 
$3000  x  .25  =    $750    A's  gain. 
$5000  x  .25  =  $1250    B's  gain. 
Proof. — Whole  gain-' 


3d  Method.— $8000  :  $2000  : :  $3000  :  A's  gain,  or  $750. 

$8000  :  $2000  : :  $5000  :  B's  gain,  or  $1250.     Hence, 

Rules. — I.  By  Fractions. — Make  each  man's  capital  the 
numerator,  and  the  irliole  capital  the  denominator  of 
a  common  fraction ;  multiply  the  whole  gain  or  loss  by 
these  fractions,  and  the  products  will  be  the  respective 
shares  of  the  gain  or  loss. 


Partnership.  161 

II.  By  Per  Cent. — Find  what  per  cent  the  gain  or  loss 
is  of  the  whole  eapital,  and  multiply  each  man's  capital 
by  it. 

III.  By  Proportion. — The  whole  capital  is  to  each  part- 
ner's capital,  as  the  whole  gain  or  loss  to  each  paHner's 
share  of  the  gain  or  loss. 

2.  A  and  B  buy  a  store  which  rents  for  $950  a  year ;  A 
advanced  $3500,  B  $4800;  how  much  rent  should  each 
receive  ? 

3.  A  and  B  form  a  partnership,  A  furnishing  $2200  and  B 
$2500 ;  they  lose  $800 ;  what  is  each  one's  share  of  the 
loss? 

^4.  The  net  gains  of  A,  B,  and  C  for  a  year  are  $12800  ;  A 
furnishes  $25000,  B  $18000,  and  0  $15000 ;  how  should  the 
profit  be  divided? 

5.  A  invested  $12000  and  B  $8000  in  a  business.  A's  share 
of  the  gain  or  loss  is  to  be  §  and  B's  -J.  At  the  close  of  the 
year  their  resources  are  $25000  in  goods  and  cash,  and  liabilities 
$15000  ;  what  is  the  net  capital,  and  what  each  partner's  share 
of  the  gain  or  loss  ? 

6.  X,  Y,  and  Z  bought  a  ship  on  speculation ;  X  put  in 
$30000,  Y  $20000,  and  Z  $15000  ;  they  sold  it  at  a  loss  of 
$7500 ;  what  was  each  man's  share  of  the  loss  ? 

7.  A,  B,  C,  and  D  form  a  partnership  with  a  capital  of 
$57000 ;  A  furnishing  $10000,  B  $12000,  C  $5000,  and  D  the 
remainder ;  they  make  15%  of  the  joint  stock ;  what  is  each 
partner's  share  of  the  profit  ?  v 

8.  The  shares  of  the  joint  stock  of  a  firm  consisting  of  three 
partners,  are  as  £,  -J,  and  J  ;  they  divide  a  profit  of  $3900 ; 
what  is  each  partner's  share  ? 

9.  A  put  $7500  and  B  $6000  into  a  land  speculation  ;  and 
A's  share  of  the  loss  was  $225  ;  what  was  B's  share  ? 

10.  Two  men  formed  a  partnership,  the  former  furnishing 
3  times  as  much  capital  as  the  latter ;  they  gained  $12500 ; 
what  was  each  one's  share  of  the  gain  ? 


168 


Percentage. 


-4-  11.  A,  B,  and  0  entered  into  partnership;  A  furnishing  £, 
B  \  and  C  the  rest  of  the  capital.  On  winding  up  the  busi- 
ness, O's  share  of  the  profit  was  $4518  ;  what  were  the  respec- 
tive dividends  of  A  and  B  ? 


383.  When  each  partner  is  allowed  to  withdraw  a  stated  sum, 
and  no  interest  account  is  kept.    (Art.  380.) 

12.  A  and  B  form  a  partnership,  investing  $6000  each,  and 
agree  to  share  the  gains  or  losses  equally.  A  drew  out  $1200 
and  B  $1000.  Kequired  the  gain  or  loss  of  each  at  the  end  of 
the  year,  their  books  showing  the  following  results : 


Resources. 

Cash $7000 

Mdse.  per  inventory 7200 

Bills  receivable 2400 

Debts  due  per  Ledger 5000 

Total  resources $21600 


Liabilities. 

Firm  owes  per  Ledger $3000 

Bills  payable 1600 

Total  liabilities $4600 


Net  capital  at  closing  is  $21600- $4600  = 

A  invested $6000 

Less  withdrawal    1200 


$17000 


A's  Cr.  balance. 


B  invested $6000 

Less  withdrawal     1000 


A's  i  net  gain  =  $3600. 


$5000  B's  Cr.  balance.  $9800 
Net  gain  of  firm  $7200 
B's  ^  net  gain  = 


A  invested $6000 

Withdrew _1200 

4800 
A's  £  net  gain 3600 

A's  net  cap.  at  closing $8400 


Proof. 

B  invested $6000 

Withdrew 1000 

5000 

B's  I-  net  gain. 3600 

B's  net  cap.  at  closing $8600 


$8400 +  $8600  =  $17000,  firm's  net  capital. 

Notes. — 1.  Amounts  withdrawn  are  sometimes  considered  resources. 
But  money  withdrawn  by  a  partner  cannot  properly  be  said  to  belong  to 
the  resources  of  the  firm. 

2.  When  a  partner  has  a  fixed  salary  it  is  generally  considered  a  part 
of  his  investment. 


Partnership  Settlements. 


163 


13.  A  and  B  formed  a  partnership  ;  A  furnished  $15000,  B 
11250,  and  agreed  that  A  should  share  J  of  the  gain  or  loss, 
and  B  f.  During  the  partnership  A  withdrew  $600  and  B 
$400.  What  were  their  gains  or  losses  at  the  close,  their 
resources  being  $21000  and  liabilities  $30000,  no  interest  acct. 
being  kept. 


OPERATION. 


Liabilities £30000 

Less  resources 24000 

Firm's  net  insolvency. ......  6000 

A's  floss 18750 

B's  §  loss 12500 

Total  loss $31250 


A's  investment $15000 

Lessarnt.  withdrawn        600  $14400 

B's  investment $11250 

Less  amt.  withdrawn        400     10850 

Firms  net  investment 25250 

Add  firm's  insolvency 6000 

Firm's  net  loss $31250 


A's  |  loss  $18750  less  net  invest.  $14400  =  $4350,  A's  net  insolvency. 
B's  f  loss  $12500  less  net  invest.  $10850  =     1650,  B's  net  insolvency. 

Proof.— $6000,  Firm's  net  insol. 


14.  A,  B,  and  C  formed  a  partnership;  A  put  in  $5000, 
B  $4000,  and  C  $2500.  A  withdrew  $1000,  B  $800,  and  C 
$500.  They  agreed  to  share  the  gain  or  loss  in  proportion  to 
their  original  investments,  no  interest  account  being  kept. 
At  the  close,  what  was  each  partner's  share  of  gain  or  loss, 
and  the  net  capital  of  each,  as  shown  by  the  following 
statement : 


Resources. 

Cash  in  bank $3475 

Mdse.  per  inventory 5150 

Bills  receivable 4225 

Debts  due  firm . . .  .    .     3150 

Total  resources $16000 


Liabilities. 

Bills  payable $3000 

Rent,  etc 700 

Debts  firm  owe 2300 

Total  liabilities $6000 


15.  A  put  $10000  into  a  partnership  and  B  $5000.  They 
agreed  to  divide  the  gain  or  loss  in  proportion  to  their  original 
investments,  and  to  keep  no  interest  account.  During  the  year 
A  withdrew  $800  and  B  $500  ;  what  was  the  net  capital  of 
each  at  the  close  of  the  year,  their  resources  being  $25800  and 
their  liabilities  $18500  ?  What  per  cent  of  their  investment 
was  the  gain  or  loss  ? 


164  Percentage, 

384.  When  one  or  two  partners  are  allowed  a  fixed  salary  and 
no  interest  account  is  kept. 

16.  A  and  B  formed  a  partnership,  agreeing  to  share  the  gains 
or  losses  according  to  their  investments;  A  furnished  $20000, 
and  was  to  receive  a  salary  of  $1000,  B  furnished  $15000,  and 
was  to  have  $750  salary  ;  what  was  the  gain  or  loss  of  each  and 
what  his  net  capital  at  the  close,  by  the  following  statement : 

Resources.  Liabilities. 

Cash  on  hand $6000  Bills  payable $14000 

Mdse.  per  inventory 5000  Rent,  etc 1500 

Bills  receivable _3500  Total  liabilities $15500 

Total  resources $14500 

Liabilities $15500 

Resources 14500 


Firm's  net  in  sol 1000 

A's  2  loss  215711 


Total  loss $37750 


A's  invest 

Add  salary 1000        $21000 

B's  invest 15000 

Add  salary 750  15750 

Firm's  net  invest 36750 

Add  firm's  net  insol 1000 

Firm's  net  loss $37750 

A's  |  loss,  $21571.43  less  net  invest.  $21000  =  $571.43  A's  net  insolvency. 
B's  f  loss,  $16178.57  less  net  invest.  $15750  =     428.57  B's    " 

Proof $1000.00  Firm's  net  insol. 

17.  A  and  B  each  invested  $6000.  A  received  a  salary  of 
$1000  a  year,  and  B  $1500  for  services.  A  drew  out  $650,  B 
$500.  What  was  each  partner's  interest  in  the  firm  at  the  end 
of  the  year,  by  the  following  statement : 

Resources $48500 

Liabilities 12500    Firm's  net  cap $36000 

A's  investment $6000 

A's  salary 1000 

7000 
Less  amt.  withdrawn 650 

A's  credit  balance 6350 

B's  investment $6000 

B's  salary 1500 

7500 
Less  amt.  withdrawn 500 

B's  credit  balance 7000        13350 


Net  gains  of  firm $22650 


Partnership  Settlements. 


165 


A's  credit  balance $6350 


B's  credit  balance $7000 

"  i  gain 11825 

"   net  capital 


"    Again 11325 

"    net  capital $17675 

385.  To  find  each  partner's  interest  at  the  end  of  the  year  or 
close  of  the  partnership. 

18.  A  and  B  formed  a  partnership  Jan.  1st,  1882,  and  agreed 
to  share  the  gains  or  losses  equally.  A's  capital  was  $6000  and 
B's  $7250  ;  each  partner  was  allowed  6%  on  his  capital  and 
charged  6%  for  the  sums  withdrawn.  March  1st,  A  withdrew 
$300;  July  9th,  $250 ;  Sept.  10th,  $200 ;  Dec.  18th,  $150.  B 
withdrew  Apr.  17th,  $100;  Aug.  4th,  $400;  Nov.  23d,  $250. 
"What  was  each  partner's  interest  in  the  business  Jan.  1st,  1883, 
their  resources  being  $26500  and  liabilities  $6000  ? 


Resources $26500 

Liabilities 6000 


$20500    Firm's  net  capital- 


A's  amt.  withdrawn  $900 ;  Av.  date  July    7th,  178  d.  to  Jan,  1st. 
B's     "             "           $750;     "        "    Aug.  27th,  127  d.     "       " 

A's  capital - $6000 

Less  withdrawn 900  $5100.00 

Int.  on  cap.  1  yr $360 

Less  int.  on  $900, 178  d 26.70  333.30 

A's  credit  balance $5433.30 

B's  capital $7250 

Less  withdrawn 750  $6500.00 

Int.  on  cap.  1  yr $485 

Less  int.  on  $750,  127  d 15.87  419.13 

B's  credit  balance $6919. 13 

Firm's  net  capital $20500.00 

A's  credit  balance $5433.30 

B's      "            "      6919.13  12352.43 

Firm's  net  gains $8147.57 

B's  credit  bal $6919.13 

"   igain 4073.781 

"  net  capital $10992.9H 


A's  credit  bal $5433.30 

"   i  gain 4073.78^ 

"   net  capital $9507.08^ 


Firm's  net  capital,  $20500. 


166 


Percentage. 


19.  C  and  D  formed  a  partnership  with  a  capital  of  $12000 
apiece.  They  agree  to  share  the  gains  or  losses  equally,  each 
receiving  interest  on  his  capital  and  paying  interest  on  all 
sums  he  withdraws.  At  the  close  of  the  year  they  had  cash  in 
bank  $8000,  merchandise  $32500,  bills  receivable  $2000.  They 
owed  bills  payable  $4000,  other  debts  $5040.  During  the  year 
C  drew  out  $2015,  the  int.  on  which  to  the  end  of  the  year  was 
$40.50.  D  drew  out  $4100,  the  int.  on  which  to  the  end  of 
the  year  was  $32.  How  much  did  they  gain  or  lose,  and  what 
was  each  partner's  net  capital  at  the  end  of  the  year  ? 

20.  A  firm  of  3  partners  commenced  business  with  a  capital 
of  $6000  each.  The  gains  and  losses  were  to  be  shared  equally, 
each  was  to  have  interest  on  his  capital  and  pay  interest  o*n 
sums  withdrawn,  which  sums  were  considered  as  taken  from 
the  gains  and  not  from  the  capital.  What  was  the  net  gain  or 
loss,  and  what  each  partner's  net  capital  at  the  end  of  the  year, 
when  their  accounts  were  as  follows  : 


Assets. 

Cash $4250.00 

Mdse 16500.00 

Bills  receivable 1000.00 

Debts  due  firm 4120.67 

Partners'  withdrawals  with  interest. 

Adrewamt 1027.72 

B     "        "  2070.11 

C     "        "   3242.04 

$32210.54 


Liabilities. 

Bills  payable $500.00 

Personal  debts 630.35 

Cap.  with  interest 19080.00 

Net  gain 12000.19 

A's±  gain...  $4000.06 
Drew  out....     1007.57 

A's  bal 2992.49 

B'sigain....  4000.06 
Drew  out....  2049.61 
B's  bal 1950.45 


C'sigain 


4000.06 


Drew  out....     3213.92 
C's  bal $786.14 


$32210.54 


21.  The  firm  of  A  &  B  formed  a  partnership  Jan.  1st  for 
1  year,  investing  $8000  each.  They  were  to  have  6%  interest 
on  their  capital  and  be  charged  6%  on  sums  withdrawn.  The 
gains  or  losses  were  to  be  shared  equally.  Apr.  4th  A  drew  out 
$500,  July  10th  $400,  and  Sept.  5th  $200.  B  drew  out  May  6th 
$700,  Aug.  12th  $300,  and  Oct.  4th  $400.  What  was  each 
partner's  net  capital  on  closing,  the  net  gains  being  $3850  ? 


Partnership  Settlements.  167 

386.  To  divide  the  gain  or  loss  in  proportion  to  each  partner's 
capital,  when  employed  for  different  periods,  or  by  Averaging 
their  investments. 

Note. — An  Average  Investment  is  a  sum  invested  for  a  certain  period, 
equivalent  to  several  investments  for  different  periods.     (Art.  348.) 

22.  A  and.  B  enter  into  partnership  ;  A  furnishes  $4000  for 
8  months,  and  B  $6000  for  4  months  ;  they  gain  $2300 ;  what 
is  each  one's  share  of  the  profit  ? 

Explanation. — In  this  case  the  profit  of  each  partner  depends  on  two 
elements,  viz. :  the  amount  of  his  capital  and  the  time  it  is  employed. 

The  Int.  of  $4000  for  8  mo.  -  Int.  $4000  x  8  =  $32000  for  1  mo. 
And     "      $6000   "  4  mo.  =    "    $6000  x  4  =  $24000   "  1  mo. 
Whole  capital  =  $56000 

They  gained  $2800;  and  $2800 -=-$56000  =  .05,  or  5%. 
$32000  x  .05  =  $1600.00,  A's  share. 
$24000  x  .05  =  $1200.00,  B's  share.     Hence,  the 

Rule. — Multiply  each  partner's  capital  by  the  time  it 
is  employed.  Consider  these  products  as  their  respective 
capitals,  and  proceed  as  in  the  last  article. 

Note. — The  object  of  multiplying  each  partner's  capital  by  the  time  it 
is  employed  is,  to  reduce  their  respective  capitals  to  equivalents  for  the 
same  time,  or  to  average  their  investments.    (Art.  353.) 

23.  A,  B,  and  C  form  a  partnership ;  A  furnishing  $1500 
for  9  mo.,  B  $1700  for  10  mo.,  and  C  $1400  for  15  months ; 
they  lose  $1600;  what  is  each  man's  share  of  the  loss  ? 

24.  Jan.  1st,  A,  B,  and  C  form  a  partnership ;  A  puts  in 
$4000,  but  after  6  mo.  withdraws  $1000 ;  B  puts  in  $3000,  and 
adds  $500  after  4  mo. ;  0  puts  in  $2000  for  the  year ;  they  gain 
$1800  ;  what  is  the  share  of  each  ? 

25.  A,  B,  and  0  began  business  Jan.  1st,  when  A  put  in 
$7500,  and  July  1st  he  put  in  $2500  more ;  B  put  in  Jan.  1st 
$12000,  and  May  1st  withdrew  $4000  ;  C  put  in  Jan.  1st 
$10000,  Aug.  1st  he  added  $3000,  and  Oct.  1st  he  withdrew  $7000. 
At  the  close  of  the  year  the  profit  was  $8500  ;  how  much  ought 
each  to  have,  the  gains  being  divided  according  to  their  average 
investment  ? 


168  Percentage. 

OPERATION. 

Jan.  1st,  A  invested   $7500  x  12  =  $90000  for  1  mo. 
July  1st,  A        «  2500  x   6  =    15000  $105000 

Jan.  1st,  B        "  12000  x  12  =  144000 

May  1st,  B  withdrew    4000  x   8=    32000    112000  $217000 
Jan.  1st,  C  invested    10000  x  12  =  120000 
Aug.  1st,  C        "  3000  x   5  =    15000    135000 

Oct.  1st,  C  withdrew    7000  x   3  =  21000    114000 

Total  average  investment  for  1  month  =  $331000 
A's  share  of  profits,  $8500  x  iff  =  $2696if f 
B's        "  "        $8500  x  iff  =  $28763434T 

C's        "  "        $8500  x  H4-  =  $2937j|f 

Proof.— $8500,  entire  profits. 

Explanation. — Each  investment  and  withdrawal  is  multiplied  by  the 
number  of  months  between  its  date  and  the  time  of  settlement.  The 
products  of  each  partner's  withdrawals  are  subtracted  from  the  products  of 
his  investments,  and  the  remainder  is  his  average  investment.  The  sum 
of  the  average  investments  is  the  denominator  and  each  separate  invest- 
ment the  numerator  of  the  fractions  which  indicate  each  partner's  share 
of  the  gain. 

Note. — The  same  result  may  be  obtained  by  either  of  the  preceding 
methods  (Art.  382).  When  the  first  method  is  used,  the  fractions  should 
be  reduced  to  their  lowest  terms. 

26.  A  and  B  formed  a  partnership  and  divided  the  gain  or 
loss  in  proportion  to  their  average  investments.  A  put  in 
$6000  for  12  months,  and  afterwards  $4000  for  6  months.  He 
withdrew  $3000  for  4  mo.,  then  $6000  for  2  mo.,  before  the 
close  of  the  partnership.  B  put  in  $7000  for  12  mo.,  then 
$6000  for  8  mo.     He  withdrew  $4000  for  5  mo.,  then  $8000  for 

2  months.    They  gained  $4560;  what  was  each  partner's  share  ? 

27.  X,  Y,  and  Z  formed  a  partnership ;  X  putting  in  $3000 
for  1  year,  Y  $4500  for  8  months,  and  Z  $5000  for  6  months ; 
they  lost  $4000  ;  what  was  each  man's  share  of  the  loss? 

28.  Three  men  hire  a  pasture  for  $87.50.  A  put  in  10  cows 
for  7  months,  B  60  sheep  for  5  months,  and  0  12  horses  for 

3  months ;    5   sheep   being  considered  equal   to   1  cow,  and 

4  horses  equal  to  5  cows  ;  how  much  should  each  pay  ? 

29.  A  and  B  are  partners,  A  putting  in  $4500  and  B  $2500 ; 
after  6  mo.  they  take  in  C  who  furnished  $10000  ;  their  gain 
for  the  year  was  $5000 ;  what  was  Mie  share  of  each  ? 


Bankruptcy.  1G9 

30.  Two  men  entered  into  speculation  and  their  profits  dur- 
ing the  year  were  $6240.  At  first  A?s  capital  was  to  B's  as  3 
to  2  ;  after  4  months  A  withdrew  £  of  his  and  B  £  of  his ;  how 
ought  the  gain  to  be  divided  ? 

31.  A  firm  commenced  business  with  a  capital  of  $15600, 
and  doubled  it  in  1  year.  A  put  in  ^  for  f  of  the  yr.,  B  -f  for 
£  of  the  yr.,  and  0  the  balance  for  f|  of  the  yr.  What  was 
each  partner's  interest  in  the  concern  at  the  end  of  the  year  ? 

32.  A  and  B  are  partners,  each  furnishing  $10000  ;  after 
4  mo.  A  took  out  $1000  and  B  $1500  ;  4  mo.  later  each  took  out 
the  same  sum  as  before,  and  at  the  end  of  the  year  the  assets 
of  the  firm  were  $15136 ;  to  what  share  was  each  entitled  ? 

33.  Three  men  form  a  partnership  and  contribute  $20000, 
$30000,  and  $40000  respectively.  A  drew  out  $3000,  B  $4000, 
and  0  $5000  a  year  and  in  3  years  the  assets  of  the  firm  were 
$120000 ;  how  much  belonged  to  each  ? 

BANKRUPTCY. 

387.  A  Bankrupt  is  a  person  who  is  insolvent,  or  unable  to 
pay  his  debts. 

388.  Bankruptcy  is  the  state  of  being  insolvent  or  a 
bankrupt. 

Note. — After  the  assets  of  a  bankrupt  have  been  applied  to  meet  his 
liabilities,  he  still  remains  liable  for  them  unless  discharged  by  a  Court 
of  Bankruptcy,  or  by  a  compromise  with  creditors. 

389.  The  Assets  of  a  bankrupt  are  the  property  in  his 
possession. 

The  Liabilities  are  his  debts. 

390.  The  Net  Proceeds  are  the  assets  less  the  expense  of 
settlement.  They  are  divided  among  the  creditors  according 
to  their  claims. 

Note. — The  claims  of  a  certain  class  of  creditors,  as  employees  and 
others,  are  paid  in  full  up  to  a  certain  amount.  These  are  called  "Pre- 
ferred Creditors." 


170 


Percentage, 


391.    To  find  each  Creditor's  Dividend,  the  Liabilities  and  Net 
Proceeds  being  given. 

l.  A  merchant  failing  in  business  made  the  following  state- 
ment: 


Liabilities. 

Notes  outstanding $1200 

A.  Booth  &  Co 2500 

Bliss  &Co 8750 

Total $12450 


Assets. 

Cash $2737 

Real  Estate 1500 

Merchandise 2950 

Total 7187 

Expenses  of  settling 215 

Net  assets $6972 

The  net  assets  $6972.00-*- $12450  liabilities  =  .56,  or  56%,  rate. 
Dividend  to  creditors  is  $1200  x  .56  =  $672  on  notes, 
$2500  x  .56  =  $1400  to  Booth  &  Co.,  and 
$8750  x  .56  =  $4900  to  Bliss  &  Co.     Hence,  the 

Rule. — Find  what  per  cent  the  net  proceeds  are  of  the 
liabilities,  and  multiply  each  creditor's  claim  by  it. 

2.  A  bankrupt  owes  A  $6500,  B  $4600,  and  D  $3800;  his 
assets  are  $5950,  and  the  expenses  of  settling  $1700  ;  what  per 
cent  and  how  much  will  each  creditor  receive  ? 

3.  A  R.  R.  Co.  went  into  bankruptcy,  owing  $48500,  and 
having  $13300  assets ;  the  expense  of  settling  was  h%  of  the 
amount  distributed  to  creditors.  What  per  cent  and  how 
much  did  a  creditor  receive  on  $8350  ?     (Art.  216.) 

4.  A  manufacturer  failed,  owing  A  $12260,  B  $13850,  and 
C  $14560  ;  his  assets  were  $28350,  and  the  expenses  of  settling 
were  $1250.  He  owed  $850  to  employees  who  were  to  be  paid 
in  full ;  what  per  cent  and  how  much  did  the  other  creditors 
receive  ? 

GENERAL  AVERAGE. 

392.  General  Average  is  the  equitable  apportionment  of 
losses  at  sea  among  the  owners  of  a  cargo,  when  the  safety  of 
the  vessel  required  a  portion  of  it  to  be  thrown  overboard. 


Notes.— 1.  The  voluntary  sacrifice  of  property  for  safety   is  called 
Jettison. 


General  Average.  17i 

2.  The  parties  whose  goods  are  sacrificed  are  not  paid  in  full,  but  bear 
their  proportion  also  for  the  loss  sustained. 

3.  Insurance  companies  bear  their  proportion  of  the  loss,  as  found  by 
general  average. 

393.  To  establish  a  valid  claim  for  a  general  average,  three 
things  must  be  made  apparent : 

1st.  An  imminent  common  peril,  and  necessity  for  sacrifice. 

2d.    A  voluntary  sacrifice  oi  apart  to  save  the  remainder. 

3d.  The  success  of  the  effort  to  save  a  part,  as  a  result  of  the 
sacrifice. 

Note. — The  jettison  is  included  in  the  contributory  interests,  and  bears 
its  proportion  of  the  loss. 

1.  A,  B,  and  C  freighted  a  vessel  with  flour  from  New  York 
to  New  Orleans;  A  had  on  board  1800  barrels,  B  1200,  and  C 
600 ;  on  her  passage  600  barrels  were  thrown  overboard. 
Beckoning  the  value  of  the  flour  at  $5.50  a  barrel,  what  was 
the  average  loss  ? 

Note. — Find  the  per  cent  of  loss  as  in  the  last  Article,  the  sum  of  the 
values  of  the  contributory  interests  being  as  the  base.     (Arts.  219,  254.) 

2.  In  a  heavy  storm,  the  master  of  a  London  packet  threw 
goods  overboard  to  the  amount  of  $15000.  The  whole  cargo 
was  valued  at  $74000,  and  the  ship  at  $38000  ;  what  per  cent 
loss  was  the  general  average  ;  and  how  much  was  A's  loss,  who 
had  goods  aboard  to  the  amount  of  $16000  V 

3.  If  an  Insurance  Co.  had  assumed  a  risk  amounting  to 
$12000,  at  2|%  on  the  vessel  and  cargo  mentioned  in  the  above 
example,  and  paid  a  general  average  loss,  what  would  have 
been  its  real  loss  by  the  disaster  ?     (Art.  215. ) 

4.  The  sloop  Huron,  from  Chicago,  carried  3000  bushels 
wheat  for  T.  Hamilton  &  Co.,  insured  in  Co.  B.  for  $3000,  at 
2% ;  2500  barrels  flour,  valued  at  $5  a  barrel,  for  G.  Standart, 
insured  in  Co.  C.  at  2\% ;  and  500  bu.  corn,  valued  at  50  cts.  a 
bu.,  for  Gardner  &  Co ,  insured  in  Co.  D.  at  \\%.  The  vessel 
was  insured  for  $25000,  \  its  value,  in  Co.  A.,  at  3%.  During  a 
storm  the  flour  was  thrown  overboard ;  what  per  cent  was  the 
general  average,  and  what  the  loss  of  each. 


(s^^ 


394.  The  arrangement  of  problems  under  different  heads, 
as  Profit  and.  Loss,  Commission,  Interest,  Proportion,  etc.,  is 
convenient  for  reference  and  review,  but  experts  perform  most 
of  their  business  calculations  by  Analysis. 

395.  No  specific  rules  can  be  given  for  the  solution  of 
problems  by  analysis.  Common  sense  and  judgment  are  the 
best  guide. 

396.  The  reasoning  in  general  proceeds  from  that  which  is 
known  or  self-evident,  to  that  which  is  required  ;  from  a  part 
to  the  whole,  or  from  the  whole  to  a  part ;  from  a  given  cause 
to  its  effect,  or  from  a  given  effect  to  its  cause. 

397.  Like  Numbers  only  can  be  compared.  When  fractions 
have  a  common  denominator,  their  numerators  are  compared 
like  integers. 

398.  In  finding  what  part  one  number  is  of  another,  the 
number  denoting  the  part  is  the  numerator  and  that  with 
which  it  is  compared  the  denominator. 

Note. — If  either  or  both  the  given  numbers  are  fractional,  they 
should  be  reduced  to  a  c.  d. ;  their  numerators  are  then  compared  like 
integers. 

l.  A  merchant  made  $8368  in  two  years,  and  the  differ- 
ence in  his  annual  gain  was  $986 ;  what  was  his  yearly 
profit  ? 

Solution. — The  sum  minus  the  difference  equals  twice  the  less  number. 
Therefore,  $8368-$986  =  $7383,  and  $7382-5-3  =  $3691,  the  less. 
And  $3691  +  $986  =  $4677,  the  greater. 


General  Analysis.  173 

2.  Bought  a  span  of  horses  and  a  carriage  for  $1856  ;  the 
•  horses  were  worth  $268  more  than  the  carriage  ;  what  was  the 

price  of  each  ? 

3.  To  what  number  must  962  be  added  3  times  to  make 
8472? 

4.  Bought  a  horse  for  $465,  and  sold  it  for  $240;  what  part 
of  the  cost  did  I  get  ? 

Solution.—  $240  =  ffg,  or  H  oi  $465  ;  hence  I  got  |f  of  $465. 

5.  What  part  of  112  yards  are  96  feet?  What  part  of 
112  rods  ? 

6.  Wliat  part  of  ^  is  -J^  ? 

Note. — Reduced  to  a  c.  d.  the  given  fractions  become  £ £  and  §§,  which 
are  like  fractions.     Now  22  is  f  §  of  35,  Ans. 

7.  If  y\  of  a  ship  cost  £273  2s.  6d.,  what  will  g%  cost  ? 

8.  What  part  of  £f  is  ^  ?  9.  What  part  of  46f  is  18|  ? 

10.  A  merchant  lost  $5367,  which  was  ^  of  his  capital ; 
what  was  his  capital  ? 

Analysis. — Since  $5367  =  T3ff  of  his  capital,  ^  of  it  was  \  of  $5367,  or 
$1789,  and  \%,  or  the  whole,  was  $17890,  Ans. 

11.  A  drover  being  asked  how  many  sheep  he  had,  replied, 
2149  are  equal  to  T7g-  of  them ;  how  many  sheep  had  he  ? 

12.  A  man  being  asked  his  age  replied,  If  you  add  to  it  its 
half,  its  third,  and  three  times  three,  the  sum  is  130;  what 
was  his  age  ? 

13.  |  of  a  number  exceeds  \  of  it  by  20;  what  is  the 
number  ? 

14.  A  real-estate  agent  sold  a  house  for  $7265  ;  what  was  his 
commission  at  3%  ? 

Solution. — Since  his  commission  on  $1  was  $TfTT,  on  $7265  it  was 
$7265  x  jf,  =  $217.95,  Ans. 

15.  A  house  valued  at  $8241  is  insured  for  f  its  value  at  \%\ 
what  is  the  premium  ? 


174  General  Analysis, 

16.  A  country  trader  buys  a  stock  of  goods  amounting  to 
$3450 ;  the  commission  charged  for  buying  was  %\%  \  bow 
much  must  he  remit  to  pay  for  the  goods  and  commission  ? 

17.  An  auctioneer  sold  a  lot  of  goods  amounting  to  $15600 
at  %\%  commission,  and  2\%  for  guaranty ;  the  charges  were, 
for  advertising  $25.50,  for  storage,  labor,  and  cartage  $34.50  ; 
how  much  was  due  the  owner  ? 

18.  A  miller  bought  a  cargo  of  wheat  for  $12600,  and  sold  it 
at  a  profit  of  15£%  ;  how  much  did  he  gain  ? 

Solution.— 15^%  is  .155  of  $1.  Therefore,  on  $12600  lie  gained 
$12600  x  .155  =  $1953,  Ans. 

19.  Bought  a  quantity  of  lumber  for  $5200  ;  paid  for  freight 
and  cartage  $85,  commission  $135.  I  gained  28%  on  the 
entire  cost ;  for  how  much  was  it  sold,  and  what  was  my 
profit  ? 

20.  If  12%  of  $97.50  be  lost,  what  amount  will  remain  ? 

21.  A  man  owning  f  of  a  bank,  sold  35%  of  his  share  ;  what 
per  cent  of  the  whole  was  left  ? 

22.  24  is  f  per  cent  of  what  number  ? 

23.  A  man  owned  -f  of  a  mine,  and  sold  f  of  his  interest  for 
$1710;  what  was  the  whole  cost? 

24.  What  is  the  interest  of  $840  for  2  yr.  8  mo.  24  d. 
at  6%? 

Analysis.— The  prin.  $840  x  .06  =  $50.40,  int.  1  yr. 

Int.  for  2  yr.  at  6%  =  $50.40  x  2  =  $100.80 
Int.  for  8  mo.  (f  yr.)  =  $50.40  x  f  =  33.60 
Int.  for  24  d.  (f  mo.)  =    $4  20  x  §  =        3.36 

Int.  for  2  yr.  8  mo.  24  d.  =  $137.76 

Or,  the  int.  of  $1  for  1  yr.  is  $.06  ;  for  2  yr.  8  mo.  24  d.  =  2\l  yr.,  it 

is  SH  x  .06,  or   41?g06,  and  the  int.  of  $840  will  be  *H**£X^M- 
=  $137.76,  Ans. 

25.  What  is  the  interest  of  $1165.50  for  5  yr.  3  mo.  9  d. 

at  n  ? 

26.  What  principal  on  interest  from  Apr.  9,  1881,  to  Sept.  5, 
1883,  will  amount  to  $1477.59,  at  7  per  cent  f 


General  Analysis.  175 

27.  If  #600  at  simple  interest  amounts  to  8684  in  2  yr.  and 
4  mo.,  what  is  the  rate  per  cent  ? 

Analysis.— $684,  arat.— $600,  prin.  =  $84,  int. 

The  interest  of  $600  for  1  yr.  at  \%    =    $6.00. 
The  interest  of  $600  for  %\  yr.  at  1  %  =  $14.00. 

Since  $14  int.  require  the  prin.  at  1%  fy  yr.,  $84  int.  for  the  same  time 
will  require  as  many  per  cent  as  $14  are  contained  times  in  $84,  or 
<j?c,  Ans. 

28.  If  $800  yield  $56  interest  in  a  certain  time,  what  will 
$390  yield  at  the  same  rate  ? 

29.  If  you  invest  $12250  in  R.  R.  stock  and  receive  an 
annual  dividend  of  $1102.50,  what  is  the  rate  of  interest  ? 

30.  In  1  yr.  4  mo.  $311.50  amounted  to  $348.88  at  simple 
interest ;  what  was  the  rate  per  cent  ? 

31.  An  investment  of  $8226.28  yields  $844.7937  annually; 
what  is  the  rate  of  interest  ? 

32.  How  long  must  $1200  be  on  interest  at  6%  to  amount  to 
$1344  ? 

33.  How  long  must  $3000  be  on  interest  at  5%  to  amount  to 
$3500  ? 

34.  At  6%  interest,  what  is  the  present  worth  of  $1500  due 
in  1  year  and  4  months  ? 

Note.— The  amt.  of  $1  for  the  time  is  $1.08. 

35.  What  is  the  present  worth  of  $4500  due  in  6  mo.,  when 
the  rate  of  interest  is  5%  ? 

36.  What  must  be  the  face  of  a  note  for  60  d.  to  be  dis- 
counted at  6%  at  a  bank,  that  the  proceeds  may  be  $1000? 

37.  What  must  be  the  face  of  a  note  for  90  d.  to  be  dis- 
counted at  a  bank  at  7$,  that  the  proceeds  may  be  $3250  ? 

38.  If  a  trader  gained  20%  on  the  cost  of  goods  by  selling 
them  for  $2150,  what  was  the  cost  ? 

39.  A  broker  sold  a  house  for  $7284  and  made  thereby  12J% ; 
what  did  it  cost  him  ? 

40.  How  much  shall  I  gain  by  borrowing  $3560  for  1  yr. 
6  mo.  10  d.  at  6$,  and  lending  it  at  7%  for  the  same  time  ? 


176  General  Analysis. 

41.  A  man  hired  a  house  for  1  yr.  at  $600  ;  after  3  mo.  he 
takes  in  his  friend  B.,  and  in  3  months  more  he  takes  his 
friend  0. ;  how  much  rent  should  each  pay  at  the  end  of  the 
year? 

42.  A  reservoir  has  3  hydrants ;  the  first  will  empty  it  in 
8  hours,  the  second  in  10,  the  third  in  12  hours ;  if  all  run 
together,  how  long  will  it  take  to  empty  it  ? 

43.  If  55  tons  of  hemp  cost  $880,  what  will  220  tons  cost  at 
the  same  rate  ? 

Analysis.— If  55  tons  cost  $880,  1  ton  cost  &  of  $880  =  $16,  and 
220  tons  cost  $16  x  220  =  $3520,  Ana. 

Or  thus,  55  tons  are  -^  of  220  tons  =  \  of  the  whole  number  of  tons. 
If  the  cost  of  \  is  $880,  the  whole  will  cost  $880  x  4  =  $3520,  Ana. 

44.  If  $500  yields  $35  interest  in  1  year,  how  much  will 
$2900  yield  in  the  same  time  ? 

45.  Bought  stock  at  par  and  sold  it  at  3%  premium,  thereby 
gaining  $750  ;  how  many  shares  of  $100  each  did  I  buy  ? 

46.  A  lawyer  received  $6.80  for  collecting  a  note  at  8$  com- 
mission ;  what  was  the  face  of  the  note  ? 

47.  How  many  times  will  a  wheel  16  ft.  6  in.  in  circumfer- 
ence, turn  round  in  running  42  miles  ? 

48.  If  I  buy  stocks  at  10$  below  par  and  sell  at  10$  pre- 
mium, what  per  cent  do  I  gain  on  my  investment  ? 

49.  In  what  time  will  $240  amount  to  $720,  at  12$  simple 
interest  ? 

50.  A  house  sold  for  $13000,  which  was  5$  advance  on  the 
cost ;  what  was  the  cost  ? 

51.  How  much  should  be  discounted  on  a  bill  of  $3725.87, 
due  in  8  mo.  10  d.,  if  paid  immediately,  money  being  worth  5$  ? 

52.  If  A  puts  in  $4000  for  8  mo.,  B  $6000  for  7  mo.,  and  0 
$3500  for  1  yr.,  and  they  gain  $2320,  what  is  each  partner's 
share  ? 

53.  A  clerk  who  engaged  to  work  for  $900  a  year,  com- 
menced at  12  o'clock  Jan.  1st,  1882,  and  left  at  noon,  the 
21st  of  May  following  ;  how  much  ought  he  to  receive  ? 


General  Analysis.  177 

54.  A  church  clock  is  set  at  12  o'clock  Saturday  night; 
Tuesday  noon  it  had  gained  3  min. ;  what  will  be  the  true 
time  when  it  strikes  8  the  following  Sunday  morning  ? 

55.  Divide  7500  into  3  parts  in  the  proportions  of  £,  -J, 
and  \. 

56.  A  man  failing  in  business  owed  $75000  ;  his  assets  were 
$14500  ;  he  owes  A  $10000,  B  $3750,  and  C  $12362.50.  How 
much  will  each  creditor  receive  ? 

57.  A  cistern  has  3  pipes  ;  the  first  can  fill  it  in  £  hour,  the 
second  can  fill  it  in  -J-  hour,  and  the  third  can  empty  it  in 
1  hour.  In  what  time  will  the  cistern  be  filled  if  they  all  run 
together  ? 

58.  A,  B,  and  C  when  in  partnership  gained  $4560;  A's 
stock  $4800  was  f  of  B's  and  B's  was  f  of  C's  ;  what  was  the 
gain  of  each  ? 

59.  A  tradesman  owes  $2400,  \  of  which  is  now  due,  \  is  due 
in  3  months,  \  in  4  months,  and  the  remainder  in  6  months  ; 
what  is  the  equated  time  of  payment  ? 

60.  What  is  the  difference  between  the  simple  and  compound 
interest  of  $800  for  1  yr.  6  mo.  6  d.,  at  %%  payable  semi- 
annually ? 

61.  A  note  of  $400  was  given  Jan.  1,  1881,  at  6%  int.,  on 
which  a  payment  of  $25  was  made  the  first  of  each  subsequent 
month  during  the  year;  what  was  due  Jan.  1,  1882  ? 

62.  A  merchant's  profits  average  15%,  and  his  losses  by  bad 
debts  amount  to  $1500;  what  is  the  amount  of  his  sales,  if  his 
net  income  is  $3100  ? 

63.  What  is  the  accurate  interest  on  $1500,  at  6%,  for  the 
months  of  July  and  August  ? 

64.  If  goods  are  marked  at  25%  advance  on  the  cost,  but  are 
sold  at  a  discount  of  16%  on  the  asking  price,  what  is  the  gain 
per  cent  ? 

65.  How  many  cords  of  wood  can  be  piled  on  }  of  an  acre  of 
land  if  the  pile  is  made  11  ft.  high  ? 

66.  A  and  B  are  partners;  A's  capital  is  twice  B's,  B  gains 
50%  and  A  loses  $4000,  when  A  has  §  as  much  as  B ;  what  was 
the  original  capital  ? 


J^ATIO 


Definitions, 

399.  Ratio  is  the  relation  of  one  number  to  another. 
Thus,  the  ratio  of  6  to  3  is  6-^-3,  and  is  equal  to  2. 

400.  The  Terms  of  a  Ratio  are  the  numbers  compared. 

401.  The  Antecedent  of  a  ratio  is  the  first  term. 

402.  The  Consequent  is  the  second  term.  The  two  terms 
together  are  called  a  Couplet. 

403.  Ratio  is  commonly  denoted  by  a  colon  ( J ),  which  is  a 
contraction  of  the  sign  of  division. 

Thus,  the  ratio  "6  :  3,"  is  equivalent  to  6  -*-  3. 

404.  Ratio  is  also  denoted  by  writing  the  consequent  under 
the  antecedent  in  the  form  of  a  fraction. 

Thus,  the  ratio  of  8  to  4  is  written  f ,  and  is  equivalent  to  8 :  4. 

405.  Only  like  numbers  can  be  compared  with  each  other. 

406.  A  Simple  Ratio  is  the  ratio  of  two  numbers,  as  8  :  4. 

407.  A  Compound  Ratio  is  the  product  of  two  or  more  sim- 
ple ratios.  They  are  commonly  denoted  by  placing  the  simple 
ratios  under  each  other. 

Thus,  4:2)         .     ft    0     _    .  ,      4. 

q    „  V  or,  4  x  9  :  2  x  3,  is  a  compound  ratio. 

408.  A  Compound  Ratio  is  reduced  to  a  simple  one  by  mak- 
ing the  product  of  the  antecedents  a  new  antecedent,  and  the 
product  of  the  consequents  a  new  consequent, 


Ratio.  179 

A  Direct  Ratio  is  the  antecedent  divided  by  the  consequent. 

409.  A  Reciprocal  or  Inverse  Ratio  is  a  direct  ratio 
inverted,  and  is  the  same  as  the  ratio  of  the  reciprocals  of  the 
two  numbers  compared. 

Tims,  the  reciprocal  of  8  to  4  is  \  to  \  —  4 : 8,  or  £ . 

Note. — The  reciprocal  of  a  ratio,  when  a  fraction  is  used,  is  expressed 
by  inverting  the  terms  of  the  fraction  which  denotes  the  simple  ratio. 
When  the  colon  is  used,  the  order  of  the  terms  is  inverted. 

410.  The  ratio  between  tivo  fractions  which  have  a  com- 
mon denominator,  is  the  same  as  the  ratio  of  their  nu- 
merators. 

Thus,  the  ratio  f  :  f  is  the  same  as  6  :  3. 

Note. — When  the  fractions  have  different  denominators,  reduce  them 
to  a  common  denominator;  then  compare  their  numerators.  Compound 
numbers  must  be  reduced  to  the  same  denomination. 

411.  Since  the  antecedent  corresponds  to  the  numerator  of  a 
fraction,  and  the  consequent  to  the  denominator,  changes  on  the 
terms  of  a  ratio  have  the  same  effect  upon  its  value  as  like 
changes  have  upon  the  terms  of  a  fraction.  (Art.  179,  Com- 
plete Graded  Arith.) 

» 

412.  The  ratio,  antecedent,  and  consequent  are  so  related  to 
each  other,  that  if  any  two  of  them  are  given  the  other  may 
be  found.     Hence,  the 

( 1.   The  Ratio  =  Antecedent -±-  Consequent. 

Formulas.  <  2.   The  Consequent  =  Antecedent  -r-  Ratio. 

1 3.   The  Antecedent  =  Conseqiient  x  Ratio. 

1.  The  consequent  is  16,  ratio  8,  what  is  the  antecedent  ? 

2.  The  antecedent  is  6§,  consequent  9,  what  is  the  ratio  ? 

3.  The  antecedent  is  15£,  ratio  9f,  what  is  the  consequent? 

4.  The  consequent  is  46,  ratio  12,  what  is  the  antecedent  ? 

5.  What  is  the  reciprocal  ratio  of  f  to  j?     Of  £  to  £  ? 


t^EOPOETIOK 


413.  Proportion  is  an  equality  of  ratios. 

Thus,  the  ratio  8 :  4  =  6  :  3,  is  a  proportion.     That  is, 

Four  quantities  are  in  proportion,  when  the  first  is  the  same  multiple  or 
part  of  the  second,  that  the  third  is  of  the  fourth. 

414.  The  Sign  of  Proportion  is  a  double  colon  ( J  J ),  or  the 
sign  (=)- 

Thus,  the  proportion  above  is  expressed  8  :  4  : :  6  :  3.  Or,  8  :  4  =  6  :  3, 
and  is  read  "  8  is  to  4  as  6  to  3,"  or  "  the  ratio  of  8  to  4  equals  the  ratio  of 
6  to  3." 

415.  The  Terms  of  a  proportion  are  the  numbers  com- 
pared. 

416.  The  Antecedents  of  a  proportion  are  the  first  and  third 
terms. 

417.  The  Consequents  are  the  second  and  fourth  terms. 

Thus,  in  the  proportion  4  : 8  : :  3  :  6,  the  4  and  3  are  the  antecedents, 
and  8  and  6  the  consequents. 

418.  The  antecedents  or  the  consequents,  or  both,  may 
have  more  than  one  element ;  but  whatever  elements  are 
contained  in  one  antecedent  must  be  contained  in  its  con- 
sequent. 

419.  In  every  proportion  there  must  be  at  least  four  terms 
expressed  or  understood ;  for,  the  equality  is  between  two  or 
more  ratios,  and  each  ratio  has  tivo  terms. 

420.  The  relation  of  the  four  terms  of  a  proportion  to  each 
other  is  such,  that  if  any  three  of  them  are  given,  the  other  or 
unknown  term  may  be  found.   . 


Proportion.  181 

421.  A  proportion  may,  however,  be  formed  from  three 
numbers,  for  one  of  the  numbers  may  be  repeated,  so  as  to 
form  ttvo  terms ;  as,  2  :  4  : :  4 :  8. 

Note. — When  a  proportion  is  formed  of  three  numbers,  the  middle 
number  is  called  a  Mean  Proportional. 

422.  The  Extremes  of  a  proportion  are  the  first  and  last 
terms. 

423.  The  Means  are  the  two  middle  terms. 

424.  Principles. — 1°.  In  every  proportion  the  product  of 
the  extremes  is  equal  to  the  product  of  the  means. 

2°.  Hie  product  of  the  extremes  divided  by  either  of  the 
means,  gives  the  other  mean. 

3°.  The  product  of  the  means  divided  by  either  extreme,  gives 
the  other  extreme. 

425.  Find  the  unknown  term  x  in  the  following : 

1.  9  :  154  =  153  :  x.  5.  130  lb.  :  x  =  $150  :  $850. 

2.  75  :  900  =  x  :  85.  6.  x  :  80  =  240  :  200. 

3.  28  :  14  =  36  :  x.  7.  10  A.  :  i  A.  =  fee  :  $14.50. 

4.  |:  3  =  8: 16,  8.  24  :  x  =  648  :  243. 

SIMPLE    PROPORTION. 

426.  Simple  Proportion  is  an  equality  of  two  simple 
ratios. 

427.  The  required  or  unknown  term  of  a  proportion  may  be 
found  either  by  considering  the  relative  magnitude  of  the 
given  terms,  or  by  comparing  them  as  causes  and  effects. 

428.  To  find  the  unknown  term  of  a  proportion,  when  the  other 
three  terms  are  given. 

I.     By   Relative  Magnitude. 

l.  If  18  chairs  cost  $54,  what  will  be  the  cost  of  144  chairs  ? 


182  Proportion. 

Analysis. — 18  chairs  are    the  statement. 

same  part  of  144  chairs,  as  $54  are  18  ch.  :  144  ch.  : :   $54  :  %x 

of  the  required  cost.     As  the  answer  ±4^4  _  x>  the  unk.nown  term. 
is    money,   make    $54    the    third  3 

term,  18  chairs  the  first  term,  and  ^-iir^  =  $432,   Am. 

144  the  second.     The  product  of       PkOOF.     ^t  =■  Ai    or    1\. 
the  means  divided   by  the  given 
extreme  gives  the  other  extreme,  or  unknown  term.     Hence,  the 

Rule. — I.  Arrange  the  numbers  so  that  the  third  term 
may  be  of  the  same  hind  as  the  answer. 

II.  When  the  answer  is  to  be  larger  than  the  third 
term,  make  the  larger  of  the  other  two  numbers  the 
second  term;  but  when  less,  -place  the  smaller  for  the 
second  term,  and  the  other  for  the  first. 

III.  Multiply  the  second  and  third  terms  together,  and 
divide  the  product  by  the  first ;  the  quotient  will  be  the 
fourth  term  or  answer. 

Notes. — 1.  The  factors  common  to  t\\e  first  and  second,  or  to  the  first 
and  third  terms,  should  be  cancelled. 

2.  The  first  and  second  terms  must  be  reduced  to  the  same  denomina- 
tion. The  third  term,  if  a  compound  number,  must  be  reduced  to  the 
lowest  denomination  it  contains. 


II.     By  Cause  and  Effect. 
429.  A  Cause  is  that  which  does  something. 

An  Effect  is  something  which  is  done. 

Notes. — 1.  Men  or  animals  and  machinery,  goods  bought  or  sold, 
money  at  interest,  time,  etc.,  are  causes;  for  the  increase  of  either, 
increases  the  effect  produced.  Work  done,  provisions  consumed,  cost  of 
goods,  etc.,  are  effects. 

2.  In  examples  of  freight,  distance  and  magnitude  may  be  regarded  as 
causes,  producing  money  for  their  effect. 

3.  A  little  practice  will  give  great  facility  in  distinguishing  between 
causes  and  effects. 


Simple  Proportion,  183 

430.  2.  If  8  men  mow  24  acres  in  1  day,  how  many  acres 
will  25  men  mow  in  the  same  time  ? 

Analysis. — In  this    example  the  statement. 

2d  effect  is  required,  which  is  an  ex-       tstC.        2d  C.  IstE.        2dE. 

trenie.     Put  X  in  its  place.  8  m.:  25  m.  : :  24  A.  :  X  A. 

8  m.  (1st  cause)  is  to  25  m.  (2d  cause)  as       (25  X  24)  -v-8  =c  75  A.,  Ans, 
24  A.  (1st  effect)  is  to  x  A.  (2d  effect). 

Since  the  product  of  the  means  equals  that  of  the  extremes,  the  prod- 
uct of  two  numbers  and  one  of  the  numbers  is  given,  to  find  the  other 
number  or  unknown  term.     (25  x  24)-s-8  =  75  A.,  Ans. 

3.  If  25  bushels  of  wheat  make  8  barrels  of  flour,  how  many 
bushels  will  be  required  to  make  54  barrels  ? 

Analysis.— In  this  example  statement. 

the  2d  cause  is  required,  which         *•*<*•        2d  c-  lstE-         2<1E. 

we  represent  by  x  bu.     The       25  bu.  :  X  bu.  : :   8  bbl.  :  54  bbl. 
product   of  the   extremes,  or      x  =  (54x25)-^8  =  175  bu.,   Ans. 
perfect  terms,  divided  by  the 
mean,  gives  the  required  term,  which  is  175  bushels.     Hence,  the 

Kule. — Make  the  first  cause  the  first  term,  the  second 
cause  the  second  term,  the  first  effect  the  third  term,  and 
the  second  effect  the  fourth  term ;  -putting  x  in  the  place t 
of  the  unknown  tej*m. 

If  the  unknown  term  is  an  extreme,  divide  the  prod- 
uct of  the  means  by  the  given  extreme  ;  if  a  mean, 
divide  the  product  of  the  extremes  by  the  given  mean, 
(Art.  424,  2°,  3°.) 

Notes. — 1.  All  the  elements  contained  in  one  antecedent  or  cause  must 
be  in  its  consequent,  and  all  the  elements  in  one  consequent  or  effect  must 
be  in  the  other  as  factors. 

2.  In  inverse  proportion,  1st  C. :  2d  C.  : :  2d  E.  :  1st  E. 

3.  In  continued  action,  causes  embrace  both  an  agent  and  time. 

4.  An  effect  may  be  a  simple  result,  or  both  a  result  and  time,  or  it  may 
embrace  length,  breadth,  and  thickness. 

4.  If  a  ship  has  sufficient  water  to  last  a  crew  of  28  men  for 
18  months,  how  long  will  it  last  25  men  ? 


18.4  Proportion. 

5.  If  18  ounces  of  silver  will  make  8  teaspoons,  how  many 
spoons  will  24  pounds  of  silver  make  ? 

6.  If  a  railroad  ear  runs  225  kilometers  in  8  hours,  how  far 
will  it  run  in  12f  hours  ? 

7.  If  20  yards  of  cloth,  £  yd.  wide,  are  required  for  a  dress, 
what  must  be  the  width  of  a  piece  12  yds.  long  to  answer  the 
same  purpose  ? 

8.  If  the  interest  of  $675.25  is  $55,625  for  1  year,  how 
much  will  be  the  interest  of  $4368.85  ? 

9.  What  cost  11  lb.  4  oz.  of  tea,  if  3  lb.  12  oz.  cost  $3.50? 

10.  Find  the  value  of  the  unknown  term  in  $4  :  x  : :  9:16. 

11.  If  I  own  f  of  a  farm  and  sell  f  of  my  share  for  $2300, 
what  is  the  value  of  the  whole  farm  at  the  same  rate  ? 

12.  If  14  acres  of  meadow  yield  32|  tons  of  hay,  what  will 
5J  acres  produce  at  the  same  rate  ? 

13.  If  36  horses  eat  92  hektoliters  of  oats  in  a  week,  how  many 
hektoliters  will  55  horses  eat  in  the  same  time  ? 

COMPOUND     PROPORTION. 

431.  Compound  Proportion  is  an  equality  between  a  com- 
pound ratio  and  a  simple  one,  or  between  two  compound 
ratios.     Thus, 

.  "     >  : :  24  :  63,  and    \     '     >  : :  j     '     >  are  compound  proportions. 

For,  7x3x24  =  2x4x63,  and  2x3x9x4  =  4x2x3x9.  It  is  read, 
' '  The  ratio  of  2  x  4  is  to  7  x  3  as  24  to  63." 

Note. — The  value  of  a  compound  ratio  equals  the  product  of  the  simple 
ratios  of  which  it  is  composed.     Thus,  £  x  §  =  §  x  |> 

432.  The  terms  of  a  compound  ratio  may  be  considered 
in  their  relations  to  each  other  as  causes  and  effects,  as  in 
Simple  Proportion. 

Notes. — 1.  All  the  terms  of  a  compound  proportion  are  given  in  pairs 
of  the  same  kind,  except  one  which  is  of  the  same  nature  as  the  term 
required. 

2.  The  order  of  the  terms  and  of  each  ratio  is  the  same  as  in  Simple 
Proportion. 


Compound  Proportion.  185 

l.  If  4  men  mow  60  acres  in  10  d.,  how  many  acres  can  6 
men  mow  in  8  days  ? 

Analysis.— In  this  problem  the  statement, 

1st  cause  is  4  men  and  10  days,  the  l8t  c-       2d  C.               1st  E.      2d  E. 

2d  cause  is  6  men  and  8  days,  the  1st  4  m.  :  6  m.  )     _           .            . 

effect  is  60  A.,  the  2d  effect  z  A.  is  10  d.    :  8  d.    )   '' ''               '' 
required.      Dividing  the  product  of 
the  means  by  the  product  of  the  extremes  gives  72  A.,  the  term  required. 

The  factors  may  be  arranged  in  2        6 

the  form  of  a    fraction,  and    the  6  X  $  X  $0 

work  much  abridged   by  cancella-  x  —      ^  x  10      =                Ans. 
tion. 


2.  If  8  men  can  dig  a  ditch  60  ft.  long,  8  ft.  wide,  and  6  ft. 
deep  in  15  d.,  how  many  days  will  24  men  require  to  dig  a  ditch 
80  ft.  long,  3  ft.  wide,  and  8  ft.  deep  ? 

Analysis.  —  In   thi  s  statement. 

problem    the    causes    and  lstc-        2dc-  lstE-        2dE 


effects  are  both  compound 


8  m.  :  24  m. 


ratios.     The  required  term  w  *"*  '  ^           i  : :  J     8  f t.  :     3  ft. 

x  is  the  2d  cause  and  is  one  lo  d.    I  X  d.      J         f     P  -ft    •     Q  ff 

of    the    means.      Dividing 

the  product  of  the  extremes  +      r-      AlA      A  ^  & 

by  that  of  the  means  gives      x  =  *  *  **  *  W  *  *  *  »  =  20  =  31  d. 

x  =  3*  days,  Am.     Hence,  U  X  00  X  $  X  6 

the  4 

Rule. — Arrange  the  causes  and  effects  as  in  Simple 
Proportion,  putting  x  in  the  place  of  the  required  term. 

When  all  the  means  are  given,  their  continued  product 
is  the  dividend  and  the  product  of  the  extremes  the 
divisor. 

When  the  extremes  are  given,  their  product  is  the 
dividend,  that  of  the  means  the  divisor,  and  the  quotient 
is  the  answer. 

Equal  factors  in  the  divisor  and  dividend  should  be 
cancelled. 

>  Notes. — 1.  The  terms  of  each  couplet  in  the  compound  ratio  must  be 
reduced  to  the  same  denomination,  and  each  term  to  the  lowest  denom- 
ination contained  in  it,  as  in  Simple  Proportion. 


186  Proportion. 

2.  When  the  same  quantity  is  an  element  of  both  causes  or  of  both 
effects,  or  when  both  antecedents  or  both  consequents  are  the  same  quan- 
tity, it  may  be  represented  by  the  figure  1. 

3.  If  the  wages  of  75  boys  for  84  days  were  $68.75,  how 
many  days  could  90  boys  be  employed  at  the  same  rate  for 
$41.25  ?. 

4.  If  25  persons  consume  300  bu.  of  wheat  in  2  years,  how 
much  will  139  persons  consume  in  6  years  ? 

5.  If  a  stack  of  hay  1 6  ft.  high  contains  12  cwt.,  what  will 
be  the  height  of  a  similar  stack  containing  6  tons  ? 

6.  If  a  man  pays  $30  for  freight  on  90  bbl.  flour  to  go  160 
miles,  what  must  he  pay  for  360  barrels  to  go  90  miles  ? 

7.  A  quarter-master  wished  to  remove  160000  lb.  of  provi- 
sions from  a  fortress  in  18  days;  it  was  found  that  in  12  days 
35  men  had  carried  away  but  25  tons,  how  many  men  would  be 
required  to  carry  the  remainder  in  6  days  ? 

8.  If  6  journeymen  make  132  pair  of  boots  in  4J  weeks, 
working  5-J  days  a  week,  and  12f  hours  per  day,  how  many  pair 
will  18  men  make  in  13|  weeks,  working  4 J  days  per  week, 
and  10  hours  per  day  ? 

9.  If  4  lbs.  of  yarn  will  make  12  yards  of  cloth  1  \  yard  wide, 
how  many  pounds  will  be  required  to  make  a  piece  200  yards 
long,  and  If  wide  ? 

10.  If  $800  will  earn  $11.50  in  168  days  at  6%,  how  much 
will  $640  earn  in  192  days  at  9%  ? 

11.  From  a  sheet  of  paper  25  in.  long  and  18  in.  wide,  a 
printer  cut  30  pages  for  a  book.  How  many  of  the  same  size 
pages  could  he  cut  from  a  sheet  24  in.  long  and  20  inches 
wide  ? 

12.  If  3  men  can  do  a  piece  of  work  in  6  days,  working  10 
hours  a  day,  how  long  will  it  take  16  men  to  do  twice  the 
amount  of  work,  when  they  work  at  it  9  hours  a  day  ? 

13.  If  2  compositors  can  set  50  pages  in  6  d.  of  10  hr.,  when 
each  page  contains  36  lines  of  48  letters,  how  many  compositors 
will  be  required  to  set  192  pages,  each  having  40  lines  of  54 
letters,  in  4  days  of  $  hours  ? 


Partitive  Proportion,  187 

14.  If  $1200  will  earn  819.20  interest  in  6  mo.  12  d.  at  6%, 
at  what  rate  will  $240  earn  $14.40  in  4  months  ? 

15.  If  100  horses  consume  a  stack  of  hay  20  ft.  long,  11  ft. 
3  in.  broad,  and  31  ft.  6  in.  high  in  9  days,  how  long  will  a 
stack  18  ft.  long,  5  ft.  broad,  and  14  ft.  high  supply  80  horses  ? 

16.  Bought  a  pile  of  stone  24  ft,  long,  12  ft.  high,  and  9  ft. 
wide  for  $120,  and  gave  a  note  for  $300  for  a  similar  pile  12  ft. 
wide  and  36  ft.  long ;  how  high  was  the  second  pile  ? 

17.  If  5  pumps,  each  having  a  length  of  stroke  of  3  ft., 
working  15  hr.  a  day  for  5  d.  empty  the  water  from  a  mine, 
what  must  be  the  stroke  of  each  of  15  pumps  which  would 
empty  the  same  mine  in  12  d.,  working  10  hr.  a  day,  the 
strokes  of  the  former  set  of  pumps  being  four  times  as  fast  as 
those  of  the  latter  ? 

PARTITIVE     PROPORTION. 

433.  Partitive  Proportion  is  dividing  a  number  into  two  or 
more  parts  which  shall  have  a  given  ratio  to  each  other. 

434.  To  divide  a  number  into  two  or  more  parts,  when  the 
ratio  of  the  parts  to  each  other  is  given. 

l.  A  and  B  divided  $396  in  the  ratio  of  5  to  7  ;  how  much 
had  each  ? 

Analysis.  — Since  A  had  5  opebation. 

parts  and  B  7,  both  had  54-7,       (396  -r-  12)  X  5  =  $165,  A's  part, 
or   12   parts.     Hence,    A  will       (396  _^_  12)  x  7  =  $231,  B's     " 
have  -/a  and  B  ^  of  the  money. 
Now  fl  of  $396  =  $165,  and  T7¥  of  $396  : 


IstC.  2dC.  IstE.  2dE. 

Or,  Sum  of  parts  :  whole  No.  : :  each  part  :  share  of  each.     Hence,  the 

Rule. — Divide  the  given  number  by  the  sum  of  the  pro- 
portional numbers,  and  multiply  the  quotient  by  each 
one's  proportional  part. 

2.  Divide  624  into  three  parts  which  shall  be  to  each  other 
as  6,  8,  and  12. 


188  Proportion. 

3.  Divide  450  shares  of  stock  among  3  persons,  in  propor- 
tion to  the  number  of  shares  owned  by  each  ;  A  holds  400,  B 
200,  and  C  300 ;  how  many  shares  will  each  receive  ? 

4.  Three  men  engaged  in  trade  agreeing  to  share  the  gains 
or  losses  in  proportion  to  their  investments ;  A's  capital  was 
$6000,  B's  $8000,  C's  $10000;  they  gained  $8800;  what  was 
each  man's  share  ? 

5.  A,  B,  0,  and  D  commenced  business  with  a  capital  of 
$18500;  A  invested  $800  less  than  B,  and  0  invested  $1000 
more  than  A,  and  D  $900  less  than  C  ;  how  much  did  each 
invest  ? 

6.  Divide  560  into  parts,  so  that  the  second  may  be  4  times 
the  first. 

Analysis. — The  1st  part +  4  times  the  1st  part  equals  5  parts.  Since  5 
parts  equal  560,  1  part  =  560  -f-  5  or  112,  and  112  x  4  =  448  the  2d  part. 

7.  Divide  the  number  582  into  4  such  parts  that  the  second 
may  be  twice  the  first,  the  third  21  more  than  the  second,  and 
the  fourth  54  more  than  the  first. 

8.  If  C  has  twice  as  much  money  as  B,  and  if  $12  be  taken 
from  A's  money,  it  will  be  equal  to  \  of  B's ;  how  much  has 
each,  the  sum  of  their  money  being  $645  ? 

9.  If  6  lbs.  of  coffee  cost  $2,40,  and  20  lbs.  of  coffee  are 
worth  12  lbs.  of  tea,  what  will  120  lbs.  of  tea  cost  ? 

10.  If  8  grammars  cost  $6.40,  and  9  grammars  are  worth 
6  geographies,  48  spellers  10  geographies,  3  arithmetics  18 
spellers,  15  readers  9  arithmetics,  how  much  will  8  readers 
cost  ? 

n.  A,  B,  and  C  are  in  partnership;  A  puts  in  \  of  the  cap- 
ital, B  T5¥,  and  C  the  remainder ;  they  gain  $2150 ;  what  is 
the  share  of  each  ? 

12.  If  |  of  A's  money  and  £  of  B's  equal  $900,  and  f  of  B's 
is  twice  §  of  A's,  what  sum  has  each  ? 

13.  A  father  divided  $18500  among  3  children,  so  that  the 
portion  of  the  second  was  greater  by  one-half  than  that  of  the 
first,  and  \  the  first  was  equal  to  \  of  the  third;  what  was  the 
share  of  each  ? 


jXCHANGE, 


435.  Exchange  in  Commerce  is  of  two  kinds,  Domestic  or 
Inland  and  Foreign. 

436.  Domestic  Exchange  is  making  payments  between 
different  places  in  the  same  country  by  Drafts,  or  Bills  of 
Exchange. 

437.  Foreign  Exchange  is  making  payments  between  places 
in  different  countries,  in  the  same  manner. 

Note. — In  commercial  law,  the  different  States  of  the  United  States  are 
considered  foreign  to  each  other.  But  for  the  purposes  of  the  present 
work  transactions  between  them  will  be  treated  under  Domestic  Exchange. 

438.  The  Par  of  Exchange  is  the  standard  by  which  the 
value  of  the  currency  of  different  countries  is  compared,  and  is 
either  intrinsic  or  commercial. 

439.  Intrinsic  Par  is  a  standard  having  a  real  and  fixed 
value  represented  by  gold  or  silver  coin. 

440.  Commercial  Par  is  a  conventional  standard,  having  any 
assumed  value  which  convenience  may  suggest. 

Note. — The  fluctuation  in  the  price  of  bills  from  their  par  value,  is 
called  the  Course  of  Exchange. 

441.  A  Bill  of  Exchange  or  Draft  is  a  written  order  direct- 
ing one  person  to  pay  another  a  certain  sum,  at  a  specified 
time. 

442.  A  Sight  Draft  is  one  payable  on  its  presentation. 

443.  A  Time  Draft  is  one  payable  at  a  specified  time  after 
date  or  presentation. 

Note — Drafts  or  Bills  of  Exchange  are  negotiable  like  promissory 
notes,  and  the  laws  respecting  them  are  essentially  the  same. 


190  Exchange. 

444.  An  Acceptance  of  a  draft  is  an  engagement  to  pay  it. 
As  evidence,  the  drawee  writes  the  word  accepted  across  the 
face  of  the  draft,  with  the  date  and  his  name. 

Note. — Days  of  Grace  are  allowed  on  time  drafts  unless  otherwise 
specified,  but  the  number  varies  in  different  countries,  from  3  to  12  days. 


DOMESTIC     EXCHANGE. 

445.   To  find   the  Cost  of  a  Draft,  when  the  Face  and  Rate  of 
Exchange  are  given. 

l.  What  cost  the  following  sight  draft,  at  2\%  premium  ? 


$27°°-  New  Orleans,  Jan.  30th,  1882. 

At  sight,  pay  to  the  order  of  James  Calkins,  twenty-seven 
hundred  dollars,  value  received,  and  charge  the  same  to  the 
account  of  Selden"  Bros.,  &  Co. 

To  S.  Bliss  &  Co.,  New  York. 

Explanation. — The  remittor  of  the  above  sight  draft  is  James 
Calkins,  who  bought  it  at  the  bank  and  had  it  made  payable  to  his  order. 
He  owes  J.  Smith  of  New  York  $2700.  He  writes  on  the  back  of  the 
draft,  "  Pay  to  the  order  of  J.  Smith,"  and  signs  his  name.  When 
Smith  receives  it  he  signs  his  name  also  on  the  back  and  takes  it  to 
S.  Bliss  &  Co.,  for  payment. 

Solution.— At  Sj%  premium,  the  cost  of  $1  draft  is  $1,025,  and  $2700 
will  cost  $1,025  x  2700  =  $2767.50,  Ans. 

2.  What  cost  a  sight  draft  on  San  Francisco  for  $2500,  at 
2\%  discount. 

Solution. — A  draft  of  $1  at  %2\%  discount  will  cost  $0,975,  and 
$2500  x  .975  =  $2437.50,  Ans.     Hence,  the 

Rule. — Multiply  the  face  of  the  draft  by  the  cost  of  $1. 

What  cost  a  sight  draft  for  What  cost  a  sight  draft  for 

3.  $8515,  at  \\%  premium  ?  9.  $4265,  at  \\%  discount? 

4.  $6845,  at  \%  premium  ?  10.  $8500,  at  \%  discount  ? 

5.  $9875,  at  \%  premium  ?  11.  $8763,  at  50^  discount? 

6.  $7365,  at  2%  premium  ?  12.  $4562,  at  75^  discount? 

7.  $3876,  at  25</>  premium?  13.  $8423,  at  \%  discount? 

8.  $8245,  at  50^  premium  ?  14.  $9654,  at  \%  discount? 


Domestic  Exchange.  191 

Notes. — 1.  On  time  drafts,  both  the  rate  of  exchange  and  the  interest 
are  commonly  included  in  the  quotation  prices.  Brokerage  is  usually 
included  in  the  rate  of  exchange. 

2.  When  the  rate  of  exchange  exceeds  the  cost  of  shipping  gold  or  cur- 
rency by  express,  one  of  them  is  sent  instead  of  drafts. 

15.  What  is  the  cost  of  the  following  time  draft,  at  1  \%  pre- 
mium, and  interest  at  Q%  ? 


$5000. 


Philadelphia,  June  4th,  1883. 


Sixty  days  after  sight,  pay  to  the  order  of  George  Wil- 
liams, five  thousand  dollars,  value  received,  and  charge  the 
same  to  the  account  of  H.  Avery  &  Co. 

To  S.  Pakkhurst,  Baltimore,  Md. 

Explanation. — The  above  time  draft,  purchased  by  G.  Williams  from 
H.  Avery  &  Co.,  is  sent  by  W.  to  a  creditor,  A.  B„  in  Baltimore,  with  the 
indorsement  "  Pay  to  the  order  of  A.  B.,"  with  signature.  When  A.  B. 
receives  it  he  takes  it  immediately  to  S.  Parkhurst,  who  writes  or  stamps 
the  word  "accepted"  across  its  face,  with  date  and  signature.  The 
maturity  of  the  draft  is  63  days  from  the  date  of  acceptance. 

Solution. — The  cost  of  a  sight  draft  of  $1,  at  1\  %  premium=$1.0125 
Subtracting  the  interest  on  $1  for  63  days  (3  d.  grace),  at  6  %  =   0.0105 

The  cost  of  $1  draft  =    1.0020 

Multiplying  by  5000 

Cost  of  draft  for  $5000 =$5010. 0000,  Ans. 

Note — 3.  Since  the  bankers  in  Philadelphia  have  the  use  of  the  money 
for  63  days  before  the  house  in  Baltimore  will  pay  the  draft,  the  interest 
for  that  time,  at  the  given  rate,  is  deducted  from  the  cost. 

16.  Find  the  cost  in  Denver  of  a  draft  on  New  York  at  90 
days  sight,  for  $6265,  at  2%  premium,  interest  being  6%  ? 

17.  Bequired  the  worth  in  Lexington,  Ky.,  of  a  draft  on  Bos- 
ton for  $4500,  at  30  days  sight,  at  1%  discount  and  interest  6%, 

18.  What  is  the  worth  of  a  draft  of  $5600  on  St.  Louis,  at 
30  days  sight,  premium  1-J$,  including  interest  ? 

19.  A  commission  merchant  in  Chicago  sold  for  a  firm  in 
Detroit  a  consignment  of  French  china.  The  sales  amounted 
to  $10500,  the  commission  was  b%  on  sales.  He  sent  a  30  days 
draft  at  \%  discount  in  payment  of  the  net  proceeds;  what  did, 
it  cost  him,  interest  being  6%  ? 


192 


Exchange. 


FOREIGN  MONEYS  OF  ACCOUNT. 

446.  The  value  of  the  money  unit  of  Foreign  Countries  in 
United  States  money  is  published  annually  by  the  Secretary  of 
the  Treasury.     The  following  is  the  Report  Jan.  1st,  1883. 


Country. 

Austria 

Belgium 

Bolivia 

Brazil 

British  America.. 

Chili 

Cuba 

Denmark 

Ecuador  

Egypt 

France 

Great  Britain.  . .  . 

Greece 

German  Empire.. 

Hay  ti 

India 

Italy 

Japan 

Liberia 

Mexico 

Netherlands 

Norway 

Peru 

Portugal 

Russia 

Sandwich  Islands 

Spain 

Sweden 

Switzerland    .... 

Tripoli » . . 

Turkey    .  .    ...    . 

U.  S.  of  Colombia 
Venezuela 


Monetary  Unit. 

Florin 

Franc. 

Boliviano 

Milreisof  1000  reis... 

Dollar 

Peso 

Peso 

Crown 

Peso 

Piaster 

Franc 

Pound  sterling 

Drachma 

Mark 

Gourde 

Rupee  of  16  annas 

Lira 

Yen 

Dollar 

Dollar. 

Florin 

Crown 

Sol 

Milreis  of  1000  reis. . . 
Rouble  of  100  copecks. 

Dollar 

Peseta  of  100  centimes. 

Crown 

Franc  of  100  centimes. 
Mahbub  of  20  piasters. 

Piaster •. . 

Peso. 

Bolivar 


Standard 

Silver. . . 
G.  and  S 
Silver... 
Gold.... 
Gold.... 
G.  and  S 
G.  and  S 
Gold.... 

Silver 

Gold 

G.  and  S, 

Gold 

G.  and  S. 

Gold 

G.  and  S. 
Silver.... 
G.  andS. 
Silver.... 
Gold.... 
Silver. . .  . 
G. and  S, 

Gold 

Silver 

Gold 

Silver 

Gold 

G.  and  S. 

Gold 

G.  and  S. 
Silver.... 

Gold 

Silver 

G. and  S. 


Value  in 
U.  S.  Money. 


.40,7 

.19,3 

.82,3 
.54,6 
$1.00 
.91,2 
.93,2 
.26,8 
.82,3 
.04,9 
.19,3 

4.86,6| 
.19,3 
.23,8 
.96,5 
.39 
.19,3 
.88,8 

1.00 
.89,4 
.40,2 
.26,8 
.82,3 

1.08 
.65,8 

1.00 
.19,3 
.26,8 
.19,3 
.74,3 
.04,4 
.82,3 
.19,3 


Foreign  Moneys.  193 

Notes. — 1.  The  Franc  of  France,  Belgium,  and  Switzerland,  the 
Peseta  of  Spain,  the  Drachma  of  Greece,  the  Lira  of  Italy,  and  the 
Bolivar  of  Venezuela  are  the  same  in  value. 

2.  The  Peso  of  Ecuador  and  of  U.  S.  of  Colombia,  the  Boliviano  of 
Bolivia,  and  the  Sol  of  Peru  are  the  same  in  value. 

3.  The  Crowns  of  Norway,  Sweden,  and  Denmark  are  also  the  same 
in  value. 

Quotations  of  Foreign   Bills  of  Exchange. 

Sterling,  60  d.,     $482$.  Reichsmarks  (4). 

sight,    $485.  For  long  sight,  .94f  @  .94^ 

Cable  transfers,  $4.85    @  $4.85 J.       For  short  sight,  .95    @  .95$. 

Commercial,        $4.80    @  $4.80$.      Amsterdam,  60  d.,  .39$. 

Francs,  60  d.,        5.23f  @    5.23$.  "  3d.  sight,  .40$. 

Notes. — 1.  Bills  at  60  days  are  generally  less  than  sight  bills,  because 
of  the  interest  on  them  for  the  time. 
(For  intrinsic  par,  see  Table,  Art.  446.) 

2.  Cable  Transfers  signify  the  method  of  sending  funds  to  persons 
abroad  by  means  of  the  Atlantic  Cable. 

Payments  are  often  effected  by  telegraph  between  distant  places  in  the 
United  States. 

3.  Commercial  Bills  are  drafts  drawn  upon  merchants. 

4.  Exchange  on  Paris  is  quoted  by  giving  the  number  of  francs  and 
centimes  to  $1.  The  same  applies  to  all  countries  where  the  franc  and  its 
equivalents  are  used. 

5.  Amsterdam  quotations  give  the  number  of  United  States  cents  to 
the  guilder  or  florin.     Intrinsic  par  of  1  guilder  =  40r8T  cents. 

6.  Quotations  in  Reichsmarks  are  based  on  the  cost  of  4  reichsmarks  ; 
hence,  .94|  @  .94$  signify  the  number  of  cents  to  be  paid  for  4  marks. 

447.  The  value  of  the  unit  of  foreign  moneys  of  account 
being  given  as  in  the  table  (Art.  446),  the  cost  and  face  of 
bills  are  easily  found  by  Analysis. 

448.  To  find  the  value  of  Sterling  money  In  U.  S.  money. 

l.  Change  £410  12s.  8-|d.  to  U.  S.  money. 

8.5d. 
12.708 


Explanation.  —  Reducing  the  12 

shillings  and  pence  to  the  decimal  20 

of  a  pound,  as  in  the  margin,  and 
multiplying  by  the  value  of  £1  as 


410.635  + 


given  in  the  table,  the   result  is      ^10.635  X  4.8665  =  11998.355. 
$1998.355,  Ans. 


194  Exchange. 


FOREIGN    EXCHANGE. 

449.  Bills  of  Foreign  Exchange  are  commonly  drawn  in  the 
money  of  the  country  in  which  they  are  payable. 

450.  A  Set  of  Exchange  consists  of  three  bills  of  the  same 
date  and  tenor,  called  First,  Second,  and  Third  of  exchange. 
They  are  sent  by  different  mails  in  order  to  save  time  in  case  of 
miscarriage.     When  one  is  paid,  the  others  are  void. 

Note. — Exchange  with  Europe  is  chiefly  done  through  the  large 
commercial  centers,  as  London,  Paris,  Geneva,  Amsterdam,  Antwerp, 
Bremen,  Vienna,  Hamburg,  Frankfort,  and  Berlin. 

451.  A  Letter  of  Credit  is  a  draft  made  by  a  banker  m  one 
country,  addressed  to  foreign  bankers,  by  which  the  holder 
may  draw  fnnds  at  different  places  in  any  amount  not  exceed- 
ing the  limits  of  the  letter  of  credit. 

Note. — Travellers  generally  prefer  letters  of  credit  to  bills  of  exchange, 
because  they  can  draw  at  any  time  and  at  different  places  such,  sums  as 
their  convenience  may  require. 

452.  Sterling  Bills  or  bills  on  Great  Britain  are  quoted  by 
giving  the  market  value  of  £1  exchange  in  dollars  and  cents. 

453.  To  find  the  Cost  of  Sterling  Bills,  when  the  Face  and 
Rate  of  Exchange  are  given. 

l.  Eequired  the  cost  of  the  following  bill  on  London,  at 
$4.8665  per  pound. 


£875  16s.  Baltimore,  Jan.  10,  1882. 

At  ten  days  sight  of  this  First  of  Exchange  {Second  and 
Third  of  same  tenor  and  date  unpaid),  pay  to  the  order 
of  Peter  Cooper,  Eight  Hundred  Seventy-five  Pounds 
Sixteen  Shillings  Sterling,  value  received,  and  charge  the  same 
to  account  of  Henry  Hayward,  Jr. 

To  James  Kent  &  Co.,  Bankers,  London. 

Analysis. — Reducing  16s.  to  decimals  of  a  pound,  the  face  of  the  bill 
£875  16s.  =  £875.8.  Since  £1  is  worth  $4.8665,  £875.8  are  worth  $4.8665 
x  875.8  =  $4262.0807,  the  cost.    Hence,  the 


Foreign  Exchange.  195 

Kule. — Reduce  the  shillings  and  pence  to  the  decimal 
of  a  pound,  and  multiply  the  face  of  the  bill  by  the  given 
rate  of  exchange.     (Art.  446.) 

2.  An  importer  owed  a  manufacturer  in  Sheffield,  Eng., 
£1740  10s.;  what  cost  a  bill  on  London  for  the  amount, 
exchange  being  $4.87-$-? 

3.  When  exchange  on  Manchester  is  $4.88,  what  cost  a  bill 
of  £3520  ? 

4.  A  merchant  in  New  York  gave  an  order  to  a  broker  to 
remit  to  Liverpool  £15000.  With  exchange  at  $4.89^  and 
brokerage  \%,  what  did  it  cost  him  in  U.  S.  money  ? 

5.  What  cost  a  bill  of  exchange  for  £2800  15s.  9d.  at  $4.85  ? 
At$4.82J? 

6.  What  cost  £3560  18s.  3d.  at  $4.80?  At  $4.89£?  At 
$4.83-|? 

454.  To  find  the  face  of  Sterling  Bills,  the  cost  and  rate  of 
exchange  being  given. 

7.  A  merchant  paid  $4256.40  for  a  sight  bill  on  London  ; 
exchange  being  $4. 86,  what  was  the  face  of  the  bill  ? 

a                 a       *Aoa    it*.      oi       i              4.86  )  $4256.40 
Analysis. — Since  $4.86  will  buy  £1  exchange,  i 

$4256.40  will  buy  as  many  pounds  as  $4.86  are  875.8 

contained  times  in  $4256.40,  or  £875.8.     (Art.  20 

153.)    Hence,  the  .  «OWK    ..  f, 

'  .  Ans.  £875, 16s. 

Ecjle. — Divide  the  cost  of  the  bill  by  the  given  rate  of 
exchange ;  the  quotient  will  be  the  face  of  the  draft. 
Reduce  the  decimals,  if  any,  to  shillings  and  pence. 
(Art.  153.) 

Note. — When  the  cost  and  face  of  the  bill  are  given,  the  rate  of 
exchange  is  found  by  dividing  the  latter  by  the  former.     (Art.  216.) 

8.  An  importer  paid  $15265.40  for  a  bill  of  exchange  on 
Birmingham;  exchange  being  $4.87,  what  was  the  face  of  the 
bill? 

9.  Paid  $25275  for  a  bill  on  Edinburgh;  exchange  being 
$4. 87 J,  what  was  the  face  of  the  bill  ? 


196  .Exchange. 

10.  Paid  $8500  for  a  bill  on  Dublin,  exchange  at  $4.88; 
what  was  its  face  ? 

n.  The  cost  of  a  bill  on  Liverpool  for  £825  16s.  6d.  was 
$3964.50  ;  what  was  the  rate  of  exchange  ? 

12.  The  cost  of  £492  17s.  6d.  was  $1850;  what  was  the 
rate  ? 

13.  On  an  invoice  of  £850,  what  is  the  difference  between 
its  valuation  at  the  Custom  House  and  an  exchange  rate  of 

$4.80?     - 

14.  At  $2946.50  for  £600,  what  was  the  rate  ? 

Note. — The  cost  of  imported  goods  is  generally  estimated  by  adding 
the  charges  of  importation  to  their  value  in  the  money  of  the  country 
from  which  they  come. 

15.  An  English  merchant  consigned  to  an  agent  in  New 
York  the  following  invoice :  188  pieces  of  broadcloth,  37J 
yards  each  ;  165  pieces  of  silk,  52  yds.  each  ;  68  pieces  velvet, 
21  yds.  each ;  the  agent  sells  the  cloths  at  $4.93  per  yard;  the 
silks  at  $1.27  ;  and  the  velvets  at  $2.62-§- ;  pays  35%  duties,  and 
charges  2\%  commission;  $83.25  for  storage,  and  sends  his 
principal  a  draft  on  the  Bank  of  England  for  the  amount ;  the 
rate  of  exchange  being  $4.85-|,  what  was  the  amount  of  the 
draft  in  sterling  money  ? 

16.  A  merchant  imports  160  pieces  of  broadcloth,  24  yd. 
each,  costing  $2.75  per  yd.  The  duties  and  other  charges 
amounted  to  $650.  What  must  be  the  face  of  a  sterling  bill 
of  exchange  to  pay  for  the  goods,  and  what  price  per  yard 
must  he  sell  them  to  make  15%  profit  ? 

455.  Bills  of  France,  Belgium,  and  Switzerland  are  quoted 
by  giving  the  value  of  $1  U.  S.  money  in  francs  and  centimes. 

Note. — Centimes  are  commonly  written  as  decimals  of  a  Franc. 

17.  Required  the  cost  of  a  bill  on  Paris  of  3000  francs, 
exchange  5.25  fr.  to  a  dollar. 

Solution.— Since  5.25  fr.  will  buy  $1  exchange,  3000  francs  w:  1  buy 
as  many  dollars  as  5.25  are  contained  times  in  3000,  or  $571  42,  Ans. 


Foreign  Exchange.  197 

18.  An  invoice  of  goods  costing  8324.50  fr.  was  passed 
through  the  Custom  House  ;  what  is  the  difference  in  U.  S. 
money  between  its  custom-house  value  and  the  exchange 
rate  5.22  ? 

19.  Paid  $600  for  a  bill  on  Geneva ;  what  was  the  face  of 
the  bill,  exchange  being  5.16  fr.  to  $1  ? 

Analysis.— If  $1  will  buy  5.16  fr.,  $600  will  buy  600  times  as  many, 
and  5.16  x  600  =  3096  francs,  Am. 

20.  Bought  a  bill  on  Havre  for  $4500;  exchange  being  5.23, 
what  was  the  face  of  the  bill  ? 

21.  What  cost  a  bill  on  Antwerp  for  1200  francs,  at  5.20  fr. 
exchange  ? 

22.  What  is  the  difference  between  exchange  at  5.24  fr.  and 
the  custom-house  value  on  a  bill  for  68000  francs  ? 

456.  Bills  ou  Germany  are  drawn  in  marks  (reichsmarks). 
They  are  quoted  by  giving  the  value  of  four  marks  in  U.  S. 
cents.     The  intrinsic  par  value  of  4  marks  is  95.2  cents. 

457.  Bills  on  Austria  and  Netherlands  are  drawn  in  florins 
or  guilders,  and  are  quoted  by  giving  the  value  of  1  florin  in 
U.  S.  cents. 

23.  An  agent  in  Amsterdam  remitted  a  draft  on  New  York 
for  which,  including  brokerage  \%,  he  paid  975  guilders; 
what  was  the  face  of  the  draft,  exchange  at  40.2  cents  to  a 
guilder  ?. 

24.  What  cost  a  bill  on  Frankfort  for  840  marks,  exchange 
being  $.94$  ? 

Analysis. — Since  4  marks  are  worth  $.945,  the  worth  of  840  marks  is 
840  times  \  of  $.945,  or  $198.45,  Arts. 

Note. — Multiply  the  exchange  value  of  4  marks  by  the  given  amount 
and  divide  the  product  by  4,  or  divide  before  multiplying. 

25.  What  cost  a  bill  on  Berlin  for  3800  marks  at  $.96 J  ? 


198  Exchange. 

NOTE. — When  the  value  of  an  invoice  at  the  Custom  House  is  required, 
multiply  the  given  amount  in  marks  by  the  intrinsic  par  of  1  mark  23.8; 
the  product  will  be  in  cents. 

26.  What  is  the  face  of  a  bill  on  Hamburg  when  exchange  is 
.94J  and  the  cost  of  a  draft  $1856  ? 

458.  The  method  of  finding  the  face  of  a  foreign  bill  of 
exchange  is  essentially  the  same  as  that  of  domestic  bills. 

27.  Eequired  the  face  of  a  bill  on  Hamburg  for  which  $2500 
was  paid,  exchange  being  95  cents. 

Analysis. — Since  95  cents  will  buy  4  marks,  $2500  will  buy  as  many 
times  4  marks  as  .95  is  contained  times  in  $2500  or  2631  j^,  and  2631^  x  4 
=  10526T6¥  marks,  Ans. 

28.  What  would  be  the  Custom  House  valuation  of  the 
same  bill  ? 

Solution.-$2500.00-j-23.8  cts.  =  10504T2T\  marks.  Ans. 

29.  Find  the  face  of  a  bill  on  Frankfort  costing  $1762  in 
gold,  exchange  at  .95 \. 

30.  Paid  $2800  for  a  bill  on  Berlin,  exchange  .93|;  what  was 
the  amount  of  the  bill  ? 

31.  What  is  the  cost  of  a  bill  of  3800  florins  on  Amsterdam, 
exchange  being  39§-  cents  to  a  florin  ? 

Analysis. — Since  1  florin  costs  39|  cents,  3800  florins  will  cost  3800 
times  as  much,  and  $.395  x  3800  =  $1501.  Hence,  the  cost  of  the  bill 
is  $1501. 

32.  What  is  the  cost  of  a  bill  of  2500  roubles  on  Russia, 
exchange  being  65.8  cents  to  a  rouble  ? 

33.  What  is  the  value  of  an  invoice  entered  at  the  Custom 
House  for  8750.50  florins  ? 

34.  A  bill  for  8500  guilders  cost  $5355.00 ;  what  was  the  rate? 

35.  Bought  at  par  375  rupees  of  India,  385  Austrian 
guilders,  850  crowns  of  Denmark,  brokerage  \%  ',  what  was  the 
cost  in  U.  S.  money  ? 

36.  Sold  954  Russian  roubles  at  par,  and  paid  \%  brokerage ; 
what  was  the  net  sum  received  ? 


Duties  or  Customs.  199 


DUTIES     OR    CUSTOMS. 

459.  Duties  or  Customs  are  taxes  imposed  by  Government 
on  imported  and  exported  merchandise. 

460.  A  Tariff  is  a  list  of  goods  alphabetically  arranged,  with 
the  rates  of  duties,  drawbacks,  etc.,  on  them,  charged  and 
allowed  on  the  importation  and  exportation  of  articles  of  for- 
eign and  domestic  produce. 

461.  The  Free  List  is  the  list  of  imported  articles  which  are 
exempt  from  duty. 

462.  Duties  are  of  two  kinds,  Specific  and  Ad  Valorem. 

A  Specific  Duty  is  a  fixed  sum  imposed  on  each  article,  ton, 
yard,  gallon,  etc.,  without  regard  to  its  value. 

An  Ad  Valorem  Duty  is  a  certain  per  cent  on  the  cost  of 
goods  in  the  country  from  which  they  are  imported. 

Note. — On  some  goods  both  a  specific  and  ad  valorem  duty  is  charged  ; 
as  on  statuary  marble  $1  per  cu.  ft.  and  25%  ;  on  woolen  goods  50  cts.  a 
pound  and  85  % . 

463.  In  estimating  specific  duties,  certain  allowances  are 
made,  called  tare,  draft,  leakage,  and  breakage. 

Tare  is  an  allowance  for  the  weight  of  the  box,  bag,  cask, 
etc.,  containing  the  goods. 

Draft  is  an  allowance  made  for  waste  and  impurities. 

Leakage  is  an  allowance  for  waste  on  liquors  imported  in 


Breakage  is  an  allowance  of  a  certain  per  cent  on  liquors 
imported  in  bottles. 

Notes. — 1.    Tare    is  calculated  either  at  the  rate  specified  in  the 
invoice,  or  at  rates  established  by  Act  of  Congress. 

2.  Leakage    is   commonly    determined    by  gauging    the    casks,   and 
Breakage  by  counting. 


200  Custom  House  Business. 

3.  In  making  these  allowances  and  in  estimating  weights  and  curren- 
cies, if  the  fraction  is  less  than  $  it  is  rejected  ;  if  $  or  more,  1  is  added. 

4.  The  Long  Ton  of  2240  pounds  is  used  in  computing  Duties. 

464.  Gross  Weight  is  the  entire  weight  of  goods  and  packages. 

Net  Weight  is  the  weight  after  all  allowances  have  been 
deducted. 

CUSTOM    HOUSE    BUSINESS. 

465.  The  United  States  are  divided  into  various  districts, 
each  of  which  has  a  Port  of  Entry  and  a  Custom  House. 

466.  A  Custom  House  is  a  building  or  office  established  by 
Government  where  duties  are  collected,  vessels  are  entered, 
cleared,  etc.  The  larger  Ports  have  a  Collector,  a  Naval 
Officer,  a  Deputy-Collector,  Surveyors,  Appraisers,  Inspectors, 
Weighers,  etc. 

467.  On  the  arrival  of  a  vessel  in  Port,  the  Master  is 
required  to  present  his  manifest  and  invoice  to  the  Collector  or 
Consul,  and  pay  his  entrance  and  clearance  fees. 

468.  A  Manifest  is  a  memorandum  signed  by  the  Master  of 
a  vessel,  giving  its  name,  its  tonnage,  its  cargo,  with  the  place 
where  he  received  it,  and  the  names  of  the  shippers  and  con- 
signees. 

469.  An  Invoice  contains  a  description  of  the  goods  with 
their  cost,  in  the  weights,  measures  and  currency  of  the 
country  from  which  they  are  imported.  The  invoice  with  its 
marketable  value,  must  be  authenticated  by  a  Consul  of  the 
U.  S.,  or  by  one  of  a  country  in  amity  with  the  United  States, 
or  by  two  respectable  resident  merchants. 

470.  Ad  Valorem  duties  are  assessed  only  on  the  actual  cost 
or  general  market  value  of  the  goods  in  the  country  from  which 
they  come.  Specific  duties,  on  the  quantity  landed.  (Art. 
462,  N.) 

Note. — The  law  has  recently  been  changed  which  made  the  dutiable 
value  of  merchandise  include  the  cost  of  transportation,  commissions,  etc. 


Duties  or  Customs.  201 

471.  The  Entrance  Fee  is  the  annual  tax  paid  for  permission 
of  a  vessel  to  enter  Port.  It  is  based  on  the  measurement,  or 
tonnage  of  the  vessel. 

472.  The  Registry  of  a  ship  is  its  enrolment  at  a  custom  house. 

473.  A  Bill  of  Lading  is  &  formal  receipt  for  goods  taken  on 
board  a  vessel,  signed  by  the  master,  binding  himself  to  deliver 
them  in  good  condition,  for  a  certain  remuneration  or 
freightage. 

Note. — Bills  of  lading  are  made  out  in  triplicates ;  one  is  sent  by  mail 
to  the  consignee,  a  second  is  sent  by  the  master  of  the  ship,  and  the  third  is 
retained  by  the  consignor  or  shipper.  In  all  cases  the  bill  of  lading  is  the 
evidence  of  shipment,  and  title  to  the  goods  shipped. 

474.  A  Bonded  Warehouse  is  a  building  for  the  storage  of 
bonded  goods  on  which  the  duties  have  not  been  paid,  but 
have  been  secured  by  bond  of  the  owner  in  double  their 
amount. 

Note. — All  goods  remaining  in  bond,  are  charged  10%  additional  duty 
after  one  year,  and  if  left  beyond  3  years,  are  regarded  as  abandoned  to 
the  government,  and  sold  under  regulations  prescribed  by  the  Secretary 
of  the  Treasury. 

475.  A  Drawback  is  money  refunded  for  import  duties 
previously  paid,  or  for  internal  revenue  tax  paid  on  such 
articles  as  fermented  liquors,  medicines,  etc.,  when  these  are 
exported. 

Excise  Duties  are  taxes  or  licenses  for  the  manufacture  or 
sale  of  certain  articles  produced  and  consumed  at  home ;  as 
tobacco,  whiskey,  etc. 

1.  A  merchant  imported  610  gallons  of  olive  oil ;  allowing 
2%  for  leakage,  what  was  the  specific  duty  at  25  cts.  per 
gallon  ? 

Solution. -2%  of  610  gal.  =  12.2  gal.,  and  610-12.2  =  597.8  gal. 
Finally,  597.8  x  .25  =  $149.45,  Ans. 

2.  What  is  the  specific  duty  on  825  lb.  soap,  at  15  cts.  a  pound  ? 


202  Duties  or  Customs. 

3.  What  is  the  duty  at  30%  ad  valorem,  on  an  invoice  of 
English  goods  amounting  to  4)1500  10s.  6d.? 

4.  Find  the  duty  on  a  bill  of  English  carpeting  amounting 
to  £6250  5s.  6d.,  at  35%  ad  valorem. 

5.  Taylor  &  Co.  imported  2  cases  of  goods,  each  weighing 
175  lbs.,  costing  £1215  10s.  and  paid  a  specific  duty  of  30  cts. 
per  pound  and  35%  ad  valorem.  What  was  the  amount  of 
duty  ?    What  did  the  goods  cost  him  ? 

6.  A.  T.  Stewart  imported  goods  from  Paris  amounting  to 
28425  francs.  What  was  the  ad  valorem  duty  at  35%,  in  United 
States  money  ? 

7.  What  is  the  duty  at  40%  on  an  invoice  of  French  jewelry, 
amounting  to  8560  francs  ? 

8.  The  value  of  an  invoice  of  French  china  is  19285  fr. ; 
what  is  its  cost  in  New  York,  at  50%  duty  ? 

9.  What  is  the  duty  on  an  invoice  of  books  from  Vienna  the 
value  of  which  was  6429  florins,  at  38%  ? 

10.  Find  the  duty  on  an  invoice  of  woolen  cloths  from 
Germany  valued  at  8437  Reichsmarks,  at  45%. 

/  n.  What  is  the  duty  on  an  invoice  of  linens  amounting  to 
£3256  sterling  at  27%,  allowing  $4.866£  to  a  pound  ? 

12.  What  is  the  duty  on  an  invoice  of  650  yd.  of  broadcloths 
which  cost  in  London  16s.  6d.  per  yard,  at  40%  ad  valorem, 
the  value  of  a  pound  sterling  being  as  above  ? 

13.  Find  the  duty  at  33%  ad  valorem,  on  1  case  of  shawls 
valued  at  £42  5s.,  1  case  of  linens  at  £37  10s.,  duty  40%;  1 
case  prints  at  £8  5s.,  duty  20% ;  incidental  expenses  £1  5s., 
commission  2|% ;  consul's  fee  15s.  What  is  the  total  cost  in 
TJ.  S.  money? 

14.  Required  the  duty  and  total  cost  of  1  case  of  French 
silks,  value  3500  francs,  duty  50%  ad  valorem  ;  1  case  velvets, 
value  28000  francs,  duty  50%,  expenses,  cartage,  shipping,  etc., 
625  francs,  and  commission  2J%. 

15.  What  is  the  duty  and  total  cost  of  2500  pieces  bleached 
calico,  33  yd.  each  in  length,  and  1J  yd.  wide ;  price  6d.  per 
yd.,  duty  4  cts.  per  sq.  yd.,  and  expenses  at  Liverpool  £65  10s.? 
What  is  the  amount  of  a  bill  of  exchange  at  $4.87  to  cover 
the  cost  ? 


Duties  or  Customs. 


203 


476.  What  is  the  total  cost  and  amount  of  duty  on  the 
following  invoice,  at  the  rate  of  50%'  for  silks  and  35%  for 
broadcloths  ? 

l.  Invoice  of  two  packages  merchandise  purchased  by  A.  J. 
Smith,  London,  for  account  and  risk  of  H.  B.  Clafltn  &  Co., 
New  York,  forwarded  per  Steamer  "  Alaska"  from  Liverpool. 


Marks. 


o> 


Nos. 


$875 


$876 


Packages  and  Contents. 


1  Case  silks,  10  p'c's,  Av.  45 

yd.  each 

Discount  6  % 

1  Case  Broadcloths,  12  p'c's, 

Av.  48  yards  each 

Discount  2|  % 


Consul's  fees . . . 
Com.  2£% 

Cost  Silks 

Charges 


Ins.  and  Freight 

Packing  and  Cartage . 
Charges  for  shipping. 

£440,  13,    8 
10,    8 


Yds. 

Price. 

£  s.  d.  \ 

450 

6,6 

576 

10,8 

2,  15,  6 

4,3 

14,0 

Cost. 


£     s.d. 

146,   5,0 

8,  15,  6 

137,    9,6 

307,    4,0 
7,  13,  7 

299, 10,  5 
137,    9,6 

3, 13,  9 


£440,13,8 


Broadcloths  . . . 
Charges 


on  £441,    4,  4 

..  £137,    9,  6 

..         7,   7,  2 

£144,16,  8 

. .  £299,10,  5 

..         7,    7,  2 

£306,17,  7 


11,    0,7 
£451,  14,  3 

£  68, 14,  9 

104, 16,  8 

10,8 

£625, 16,  4 

Or,  $3045.53  ) 

Duties  £173,  11,  5  at  $4.8665  =  $842.92  \ 


Duty  on  Silks  50% 

"     Broadcloths  35%.. 
Consul's  fees 

Total  cost 


Note. — Each  invoice  is  accompanied  by  a  proper  Bill  of  Lading,  signed 
by  the  master  of  the  vessel,  stating  the  number  of  boxes  or  packages 
received,  their  marks,  weight,  and  size,  the  names  of  the  shipper  and 
consignee,  the  prices  charged  for  freight,  primage,  etc. 


204  Custom  House  Business. 


IMPORT    ENTRIES. 

477.  Goods  are  entered  at  the  Custom  House  by  marks  and 
numbers  which  should  correspond  to  those  on  the  Invoice  and 
Bill  of  Lading. 

478.  The  principal  entries  are 

1.  Merchandise  for  immediate  consumption. 

2.  Merchandise  for  storage  in  a  Bonded  Warehouse. 

3.  Merchandise  for  immediate   transportation  in   bond  to 

another  part  of  the  country. 

4.  Merchandise    for    transportation  in  bond  to  a  foreign 

country. 

5.  Merchandise  for  export  of  imported  goods,  or  of  goods 

made  in  this  Country,  for  the  benefit  of  a  Drawback. 

Course  of  an  Import  Entry  in  the  New  York  Custom  House. 

1.  The  Entry  is  made  in  duplicate,  one  copy  for  the  Collec- 
tor's Office,  the  other  for  the  Naval  Office.  It  is  a  fair 
statement  of  the  cost  of  the  goods  mentioned  in  a  foreign 
invoice,  the  name  of  the  Importer,  name  of  the  vessel,  date 
of  arrival,  etc. 

2.  The  Collector's  Entry  Clerk  endorses  the  Invoice  with 
the  value  of  the  goods  in  the  currency  of  the  country  from 
which  they  were  imported,  notes  the  rates  of  duty,  the  deduc- 
tions to  be  made,  etc.,  and  places  the  Collector's  Stamp  on  it, 
which  notes  the  name  of  the  vessel  and  date  of  arrival.  He 
then  marks  the  duty  on  the  face  of  the  Collector's  copy  of 
entry,  and  makes  out  a  Permit  for  the  goods  mentioned  in  the 
Entry  to  be  landed. 

3.  The  entry  is  then  taken  to  a  Record  Clerk  in  the 
Collector's  Office,  who  charges  it  to  the  Naval  Officer.  The 
Naval  Office  Entry  Clerk  examines  the  work  of  the  Collector's 
Entry  Clerk,  and  if  correct,  endorses  it  and  checks  the  permit. 
The  entry  is  returned  to  the  Record  Clerk,  who  charges  it  to 
the  Deputy  Collector. 


Import  Entries.  205 

4.  The  Deputy  Collector  sees  that  the  oath  on  the  entry  is 
taken,  designates  the  packages  to  be  sent  to  the  public  store 
for  examination,  signs  each  invoice  under  the  steamer  stamp 
and  the  numbers  of  packages,  and  returns  the  entry  to  the 
Record  Clerk,  who  charges  it  to  the  Bond  Clerk  for  the  draw- 
ing of  a  Bond  if  necessary.  The  entry  is  then  sent  to  the 
Delivery  Clerk  for  the  Importer. 

5.  The  Importer  takes  the  entry  to  the  Cashier's  Office  for 
the  payment  of  duty.  The  Cashier  checks  the  duty  statement 
of  the  Collector's  Entry  Clerk,  etc.,  and  gives  the  Importer  the 
permit  and  the  Naval  Office  copy  of  entry. 

6.  The  Importer  presents  copy  of  entry,  etc.,  to  Naval 
Officer,  who  checks  the  papers,  records  payment  of  duty,  and 
gives  the  Importer  a  permit  signed  by  himself  and  the  Deputy 
Collector.  The  Importer  then  presents  the  permit  at  the  store 
where  the  goods  are,  pays  storage,  and  receives  packages  not 
marked  for  appraiser. 

7.  The  Appraiser,  with  the  designated  package  before  him, 
compares  the  goods  in  it  with  the  invoice,  verifies  and 
determines  the  quantity  and  value  thereof,  and  makes  his 
return  to  the  Collector. 

8.  The  entry  and  invoice  are  charged  to  an  amendment  or 
liquidating  clerk,  who  in  accordance  with  the  Appraiser's 
report,  makes  up  a  statement  of  the  duty  as  it  should  be, 
in  the  invoice.  If  the  ascertained  duty  is  found  to  be  less  than 
that  originally  paid  by  the  Importer,  the  excess  is  refunded; 
if  greater,  the  deficit  must  be  supplied.     . 

9.  At  the  closing  of  a  vessel's  account,  all  the  entries,  with 
the  manifest  of  the  cargo  and  the  Inspector's  return,  are 
placed  on  file. 

Note.— Much  of  the  labor  of  making  entries,  obtaining  permits,  etc., 
is  done  through  Custom  House  Brokers,  who  are  familiar  with  the 
necessary  steps. 


206  Banks  and  Banking. 


BANKS     AND     BANKING. 

479.  Banks  are  Incorporated  Institutions  which  deal  in 
money.     There  are  two  classes,  National  and  State-banks. 

480.  Banking  has  three  departments  of  business  : 

1st.  Receiving  money  for  safe  keeping,  subject  to  the  order 
of  the  depositor. 

2d.  Loaning  money,  discounting  notes,  drafts,  etc. 

3d.  Issuing  notes  or  bills  for  circulation. 

481.  The  Income  of  Banks  is  chiefly  derived  from  loans  and 
circulating  notes. 

482.  Banks  make  no  charge  for  keeping  deposits,  and  pay 
no  interest  on  them,  except  in  rare  cases,  at  a  low  rate.  The 
privilege  of  loaning  a  portion  of  them  is  a  large  source  of 
income,  and  ample  equivalent  for  the  care  and  responsibility. 

Notes. — 1.  According  to  the  laws  of  the  U.  S.,  Banking  Associations 
may  be  formed  of  any  number  of  persons  not  less  than  five. 

2.  No  association  may  be  organized  with  a  capital  less  than  $100000, 
with  the  exception  that  in  places  whose  population  does  not  exceed  6000, 
they  may  be  formed  with  the  approval  of  the  Secretary  of  the  Treasury, 
with  a  capital  of  $50000. 

3.  In  cities  the  population  of  which  exceeds  50000,  the  capital  must 
not  be  less  than  $200000,  the  stock  being  divided  into  shares  of  $100. 

483.  A  National  Bank  is  required  to  transfer  and  deliver  to 
the  U.  S.  Treasurer  an  amount  of  Kegistered  Bonds  not  less 
than  one-third  of  the  capital  stock  paid  in.  These  are  held  as 
security  for  the  circulating  notes  delivered  to  the  banks  depos- 
iting them. 

Notes. — 1.  Banks  having  a  capital  of  $500000  are  limited  in  their 
circulation  to  90%  of  the  par  value  of  the  registered  bonds  deposited  at 
Washington  ;  those  having  a  capital  between  $500000  and  $1000000  to 
80%;    between  $1000000  and   $3000000  to  75%,  and  above    $3000000 

to  eo%, 


Banks  and  Banking.  207 

2.  By  act  of  July  12th,  1870,  no  National  Bank  organized  after  that 
date  can  have  a  circulation  above  $500000. 

3.  A  Bank  reducing  its  circulation  may  deposit  with  the  Treasurer, 
legal  tenders  or  specie  in  sums  of  not  less  than  #9000,  and  withdraw  a 
proportionate  amount  of  the  bonds  previously  deposited. 

484.  National  Bank  notes  are  redeemable  in  lawful  money 
by  the  banks  which  issue  them,  and  by  the  Treasurer  of  the 
United  States. 

Note.— By  act  of  June,  1874,  every  National  Bank  is  required  to  keep 
on  deposit  in  the  treasury  of  the  U.  S.,  a  sum  equal  to  5%  of  its  circula- 
tion for  redeeming  its  bills. 

485.  A  Reserve  Fund  equal  to  25%  of  their  deposits,  is 
required  to  be  kept  by  National  Banks  in  the  cities  of  New 
York,  Boston,  Philadelphia,  Albany,  Baltimore,  Pittsburgh, 
Washington,  New  Orleans,  Louisville,  St.  Louis,  Cleveland, 
Detroit,  Chicago,  Milwaukee,  and  San  Francisco,  and  15%  by 
all  other  National  Banks. 

Note. — These  are  called  '"  Reser ve  Cities,"  and  the  excess  above  the 
requirements  is  called  the  Surplus  Reserve. 

486.  A  Surplus  Fund,  of  the  net  earnings  of  the  Bank,  is 
also  required  by  law  to  be  set  aside,  before  the  usual  semi- 
annual dividends  are  declared,  until  this  fund  amounts  to  20$ 
of  the  capital. 

487.  An  Annual  Tax  of  1%  is  paid  to  the  United  States  by 
National  Banks  on  the  average  amount  of  their  circulation. 

Notes. — 1.  The  circulation  of  State  Bank  Notes  ceased  after  Aug.  1, 
1866,  when  a  tax  of  10  Jo  was  imposed  by  Congress  upon  each  issue. 

2.  A  Stockholder  of  a  National  Bank  is  liable  for  an  amount  equal  to 
the  par  value  of  the  Stock  he  holds. 

3.  The  Revised  Statutes  require  National  Banks  which  go  into  voluntary 
liquidation,  to  deposit  in  the  Treasury  within  six  months,  an  amount  of 
lawful  money  equal  to  their  outstanding  circulation. 

The  law  also  requires  that  a  sufficient  amount,  thus  deposited  for  the 
payment  of  circulating  notes,  must  remain  in  the  Treasury  until  the  last 
outstanding  note  shall  have  been  presented.  Hence,  it  will  be  seen  the 
Government  derives  the  benefit  of  notes  which  are  lost  or  destroyed  by 
fire  and  water. 


208 


Bank  Account  Current 


4.  Savings  Banks  and  private  bankers  do  not  issue  notes  for  cir- 
culation. 

[For  the  organization  and  regulation  of  National  Banks,  see  Revised 
Statutes  of  U.  8.,  and  for  State  Banks,  the  laws  of  the  different  States.] 

Exam  ples. 

488.  l.  What  amount  of  Bank  Notes  is  a  National  Bank 
allowed  to  issue,  which  deposits  $500000  in  U.  S.  Bonds  to 
secure  its  circulation  ?  What  is  its  redemption  fund?  (Arts. 
484,  483.) 

2.  If  a  National  Bank  reducing  its  circulation,  deposits  with 
the  U.  S.  Treasurer  $27000  in  legal  tenders,  and  sells  the  Bonds 
withdrawn  at  115-J,  what  are  the  proceeds  ?    (Art.  483,  N.  3.) 

3.  What  is  the  semi-annual  tax  upon  a  National  Bank 
whose  average  circulation  is  $925460  ? 

4.  A  capitalist  has  on  deposit  $450000,  of  which  lh%  is  coin, 
45%  greenbacks,  and  the  balance  is  National  Bank  notes ;  what 
is  the  value  of  the  bank  notes  ? 

5.  A  bank  having  failed  was  placed  in  the  hands  of  a 
Eeceiver,  who  declared  a  dividend  of  45%  in  favor  of  the 
depositors.  A's  balance  was  $6526.50,  B's  $8417.95,  and  C's 
$4562.87  ;  how  much  did  each  receive  ? 


Bank    Account    Current. 

489.    l.  Daily  balances  at  6%  interest,  to  Apr.  26,  1883. 


Bank  Account  Current. 


1883. 

Dr. 

Cr. 

Jan.   1 

800 

5 

300 

"   31 

200 

Feb.   6 

300 

March  4 

500 

Apr.   8 

100 

"   16 

300 

"   26 

Bal.  1113.28 

Int.  13.28 

$1813.28 

$1813.28 

Daily  Balances. 


Items. 

800 
500 
700 
400 
900 
800 
1100 


Days, 
x  4  = 
x26  = 
x  6  = 
x26  = 
x35  = 
x  8  = 
xl0  = 

Int.  at  Q% 


Products. 


3200 
13000 

4200 
10400 
31500 

6400 
11000 


6  )  79700 
$13,283 


Bank  Checks. 


209 


Explanation. — On  J.an.  1,  $800  were  credited,  and  remained  till  the 
5th,  when  $300  were  debited."  $800  being  on  int.  4  d.,  the  product  is 
3200,  that  is,  the  int.  of  $800  for  4  d.  =  the  int.  of  $3200  for  1  day.  A 
debt  of  $300  being  made  Jan.  5,  there  remained  a  balance  of  $500  on  int. 
till  the  31st,  or  26  d.,  when  a  credit  of  $200  is  added,  making  $700  till 
Feb.  6,  etc.  The  int.  by  Art.  284,  is  $13.28,  which  is  added  to  the  credit 
side  of  the  account.     The  bal.  due  is  $1113.28.     Hence,  the 

Rule. — Multiply  the  debit  and  credit  balance  for  each 
day,  by  the  number  of  days  between  it  and  the  next  debit 
or  credit ;  add  the  products  and  find  interest  by  Art.  284. 

Notes. — 1.  The  balance  of  interest  must  be  entered  on  the  debit  or 
credit  side  of  the  account  as  the  case  may  be,  after  which  it  draws  interest 
like  the  other  items. 

2.  If  the  balance  of  items  is  sometimes  credit  and  sometimes  debit, 
take  the  balance  of  products  before  dividing. 

2.  What  is  the  balance  due  on  March  1st,  for  the  following 
account  current  at  5%  ? 

The  National  Exchange  Bank,  in  acct.  with  S.  S.  Carlisle. 


Bank  Account  Current. 

Daily  Balances. 

Products. 

1833. 

Dr. 

Cr. 

Dr. 

Cr. 

Days. 

Dr. 

Cr. 

Jan.   1 

200 

"   18 

150 

"   28 

250 

"   31 

125 

Feb.   4 

150 

225 

"   12 

250 

BANK     CHECKS. 

490.  A  Check  is  an  order  for  money  drawn  on  a  Bank  or 
Banker,  payable  at  sight.* 

491.  When  a  check  is  drawn  payable  to  bearer,  it  is  trans- 
ferable without  endorsement;  when  drawn  payable  to  a 
person  named,  or  his  order,  it  must  be  endorsed  by  the  person 
to  whom  it  is  made  payable. 

*  The  law  requiring  that  every  check  have  a  two-cent  revenue  stamp  placed  upon  it, 
was  repealed  July  1st,  1883. 


210  Bank  Checks. 

Notes. — 1.  The  payment  of  a  check  may  be  countermanded  by  the 
drawer,  at  any  time  before  it  is  paid  or  accepted  by  the  Bank. 

2.  The  holder  of  a  check  should  present  it  without  unnecessary  delay, 
otherwise,  if  the  Bank  should  fail,  the  drawer  will  not  be  responsible. 

3.  A  check  should  be  dated  on  the  day  it  is  drawn,  and  state  the  day 
when  it  is  to  be  paid,  if  payable  in  the  future. 

4.  The  amount  of  a  check  should  always  be  written  in  words,  and  the 
same  amount  in  figures  placed  in  the  left-hand  corner  at  the  bottom,  the 
cents  being  written  in  the  form  of  a  common  fraction,  as  §8T%%. 

492.  A  Certified  Check  is  one  upon  which  the  Paying  Tel- 
ler or  Cashier  writes  or  stamps  the  word  "Certified"  or 
"Good/'  and  under  it  his  signature.  The  bank  thus  guarantees 
payment. 


JTo.   873.  JJew  York,  Oct.  29,    1883. 

®lje    €l)emical   National    Bank.^ 

(Pay  to Alfred  J.  Pouch  J$    w „  or  Order 

Three  Thousand ^L-Q^ollars 

^  -V.  W.  Hunter. 

4* 


493.  A  Certificate  of  Deposit  is  a  written  or  printed  state- 
ment issued  by  a  Bank,  certifying  that  a  certain  person  has 
deposited  in  it  a  specified  amount  of  money. 


Brooklyn,   Qec.   12,   1883. 

(Commercial   Bank. 

George  Brown  has  deposited  in  this  l^ank.  Four 
Hundred  Dollars  to  the  credit  of  Himself,  pay- 
able on  the  return  of  this  Certificate,  properly  endorsed. 

John  J.    Vail,    Cashier. 


Note. — Certified  checks  and  certificates  of  deposit  are  often  used  in 
making  remittances,  instead  of  drafts. 


Clearing  Houses.  211 


CLEARING-    HOUSES. 

494.  A  Clearing  House  is  an  Association  of  Banks,  whose 
representatives  meet  for  the  purpose  of  daily  exchanges  of 
checks  and  drafts,  and  the  settlement  of  balances. 

495.  The  New  York  Clearing  House  is  composed  of  45  Na- 
tional Banks,  12  State  Banks,  and  the  U.  S.  Sub-Treasury  at 
New  York.  The  other  city  banks,  both  National  and  State, 
make  their  exchanges  through  the  agency  of  some  member  of 
this  Association. 

496.  The  New  York  Clearing  House,  established  in  1853, 
is  the  oldest  institution  of  the  kind  in  this  country.  Since 
that  time  22  others  have  been  established  in  different  cities. 

497.  Each  bank  is  represented  every  morning  by  a  messen- 
ger and  a  settling  clerk.  The  former  brings  the  checks,  drafts, 
etc.,  upon  the  other  banks,  which  his  bank  received  the  day 
previous.  These  are  called  the  " exchanges"  and  are  assorted 
for  each  bank  and  placed  in  envelopes.  On  the  outside  of 
each  envelope  is  a  slip  on  which  is  listed  the  amounts  of  the 
various  items  which  it  contains.  These  envelopes  are  arranged 
in  the  same  order  as  the  desks  for  the  several  banks. 

498.  At  a  signal  from  a  bell  struck  at  ten  o'clock  precisely, 
each  messenger  moves  forward  to  the  desk  next  his  own,  and 
delivers  the  envelopes  containing  the  checks,  etc.,  for  the 
Bank  represented  by  that  desk,  to  the  clerk  on  the  inside. 
The  clerk  receiving  it,  signs  and  returns  it  to  the  messenger, 
who  immediately  passes  to  the  next  desk,  delivering  the 
exchanges  as  before,  and  passes  on  until  he  has  reached  his 
own  desk  again,  having  delivered  his  entire  exchanges  for  all 
the  Banks.     This  occupies  about  ten  minutes. 

499.  The  messengers  then  receive  from  their  several  clerks 
the  envelopes  containing  the  exchanges,  and  return  to  their 
Banks  reporting  their  condition.  The  clerks  then  report  to 
the  Assistant  .Manager  the  amount  they  have  received.  They 
are  allowed  forty-five  minutes  after  the  delivery  of  the 
exchanges  to  enter  and  prove  their  work. 


212  .  Savings  Banks. 

500.  The  debit  Banks  are  required  to  pay  their  balances  to 
the  Manager  before  half-past  one  o'clock  the  same  da}',  and 
immediately  after  that  hour  the  credit  Banks  respectively 
receive  the  amounts  due  them. 

Notes. — 1.  A  record  is  kept  of  the  daily  transactions  of  each  Bank, 
and  a  statement  of  the  loans,  specie,  legal  tenders,  deposits  and  circulation 
made  weekly  to  the  Manager  of  the  Clearing  House,  so  that  the  move- 
ment of  each  Bank  can  be  determined,  and  its  condition  pretty  accurately 
estimated. 

2.  The  rapidity  with  which  exchanges  are  made  by  this  method  is  a 
marvel.  The  business  of  a  single  day  has  amounted  to  $295,821,422, 
and  the  exchanges  during  the  year  preceding  Oct.  1,  1881,  exceeded 
$48,000,000,000. 

SAVINGS    BANKS. 

501.  Savings  Banks  are  institutions  which  receive  small 
sums  of  money  on  deposit,  and  place  them  at  interest  for  the 
benefit  of  the  depositors. 

502.  They  usually  declare  a  dividend  of  the  interest  due  the 
depositors,  semi-annually,  on  the  first  days  of  January  and 
July,  which,  if  not  withdrawn,  is  passed  to  the  credit  of  the 
depositor  on  the  books  of  the  Bank,  and  bears  interest  the 
same  as  a  new  deposit.  Hence,  Savings  Banks  pay  Compound 
Interest. 

503.  Some  Savings  Banks  allow  interest  to  commence  on 
deposits  on  the  1st  day  of  Jan.,  April,  July,  and  October. 

Others,  when  deposits  are  made  on  or  before  the  1st  day  of 
any  month,  allow  interest  to  commence  on  the  1st  day  of  that 
month.  This  method  is  preferable  for  persons  having  a  small 
income. 

Notes. — 1.  No  interest  is  allowed  on  any  sum  withdrawn  before  the 
1st  day  of  Jan.  or  July  for  the  time  between  the  last  dividend  and  the 
withdrawal,  and  no  interest  is  allowed  on  fractions  of  a  dollar.  The 
smallest  balance  remaining  on  deposit  the  entire  term  is  entitled  to 
interest. 

2.  Deposits  are  usually  paid  on  demand,  though  the  Bank  is  entitled 
by  law  to  60  or  90  days  notice. 


Savings  Banks.  213 

504.  The  laws  of  the  State  of  N.  Y.  do  not  allow  Savings 
Banks  to  have  on  deposit  for  one  individual  a  sum  exceeding 
$3000,  exclusive  of  accrued  interest,  unless  such  deposit  was 
made  before  May  17th,  1875,  or  by  order  of  a  court  of  record, 
or  of  a  Surrogate. 

Notes. — 1.  Savings  Banks  are  restricted  to  5%  per  annum  regular 
interest;  but  if  their  surplus  earnings  amount  to  15%  of  their  deposits, 
they  are  required  to  declare  an  extra  dividend  once  in  3  years. 

2.  Savings  Banks  in  this  State  are  allowed  to  pay  interest  on  sums 
deposited  during  the  first  ten  days  of  Jan.  and  July,  and  the  first  three 
days  of  April  and  October  from  the  first  of  these  months. 

505.  In  the  following  examples  deposits  draw  interest  from 
the  1st  of  Jan.,  April,  July,  and  October,  at  5%,  unless  other- 
wise mentioned. 

l.  A  man  deposited  in  a  Savings  Bank,  July  1,  1882,  $175  ; 
how  much  interest  should  be  credited  him  Jan.  1,  1883  ? 


and  $175  x  .02^  =  $4.37* ,  Am. 

2.  A  man  deposited  $320  in  a  Savings  Bank  Jan.  1,  1881, 
and  July  1,  $240  ;  how  much  was  due  him  Jan.  1,  1882,  allow- 
ing 4%  interest  ? 

Analysis.— July  1,  Int.  on  $320  (6  mo.)  =  320  x  .02  =  $6.40. 

New  Principal  July  1  =  $320  +  $240  +  $6.40  =  $566.40 

Int.  6  mo.,  Jan.  1  *      =  ($566  x  .02)  =      11.32 

Amt.  due  Jan.  1, 1882  =  $577.72 

Note. — Though  interest  is  not  reckoned  on  the  fractional  parts  of  a 
dollar,  in  finding  the  amount  at  the  close  of  a  year  these  are  included. 

3.  Jan.  1,  1880,  a  clerk  deposited  in  a  Savings  Bank  $150 ; 
March  12th,  $48;  June  17th,  $125;  and  Sept.  30th,  $150. 
Withdrew  Apr.  10th,  $25;  July  12th,  $34;  Oct.  10th,  $50; 
what  was  the  balance  due  Jan.  1st,  1881,  int.  4%  quarterly  ? 

Note. — In  order  to  determine  more  easily  the  quarterly  balances 
entitled  to  interest,  the  account  may.  be  arranged  in  the  following  form, 
showing  the  amount  due  at  each  regular  interval,  the  time,  and  the  int. 
on  the  successive  amounts. 


214 


Savings  Banks. 


ir  * 


Date. 

Deposits. 

Drafts. 

I 

Bal. 

Time. 

\      Int.  4%. 

1880. 

Jan.        1 
March  12 
Apr.      10 

150 

48 

125 
3 

150 

6 

$482. 

23 

34 

57- 

%5 

34 
50 

-$109 

=  $c 

150 

173 

267 
3G7 

173.57 

3  mo. 
3  mo. 

3  mo. 
3  mo. 

Ans. 

1.50 
1.73 

June    17 
July  int. 
12 
Sept.     30 
Oct.      10 

3.23 

2.67 
3.67 

July 

1881. 

Jan.        1  int. 

6.34 

J  a  n. 

Explanation.— $150  draws  int.  3  mo.  The  2d  dep.  ($48-  $25)  +  $150 
(Apr.  bal.)  =  $173  draws  int.  3  mo.  3d  deposit  ($125  +  $3  July  int.  —$34, 
dft.)  +  $173  (July  bal.)  =  $267  draws  int.  3  mo.  4th  deposit  ($150-$50, 
dft.)  -f  $267  (Oct.  bal.)  =  $367  on  int.  3  mo.  The  sum  of  deposits  with 
interest,  less  the  sum  of  drafts  gives  the  balance  due. 

4.  A  deposited  Jan.  1,  1881,  $125 ;  March  15,  $140  ;  July  5, 
$65.  He  withdrew  Feb.  15,  1881,  $30;  Apr.  10,  $12;  Oct.  15, 
$20.  What  was  due  Jan.  1,  1882,  interest  being  ±%,  payable 
quarterly  ? 


Date. 

Deposits. 

Drafts. 

Balances, 

1881. 

* 

Jan.     1 

$125 

1 

Feb.  15 

$30     | 

|    $95 

• 

Mar.  15 

140 

Jj-                  • . 

- 

Apr.  10 

12 

128 

*H£ 

* 

*.  1.90  (6  mo.) 
•'    1.28  (3  mo.) 

July    5 

65 

$226.18  due,  July  1, 

1881. 

Oct.  15 

20- 

45                        .    . 

1882. 

' 

Jan.     1    Int. 

5.42  (6  mo.) 

$276.60  Amt.  due. 

Savings  Banks. 


215 


Note.— The  drafts  are  usually  deducted  from  the  last  deposits  made. 
Thus,  the  draft  of  $30  taken  from  $125,  leaves  a  bal.  of  $95  on  int. 
from  Jan.  1.  The  draft  of  $12,  Apr.  10th,  leaves  $128  on  int.  from 
Apr.  1,  etc.     (Art.  504,  N.  2.) 

5.  Jan.  1,"  1883,  B  deposited  $120  in  a  Savings  Bank; 
Feb.  20,  $60  ;  Apr.  1,  $150  ;  May  30,  $80 ;  what  interest  pay- 
able semi-annually  at  4$  was  due  July  1,  1883  ? 

6.  On  the  4th  of  Jan.,  1881,  a  mechanic  deposited  $84  in  a 
Savings  Bank  ;  March  25,  $50  ;  Oct.  9,  $96.  He  withdrew 
May  1,  $12,  and  on  the  20th  of  Oct.,  $21 ;  allowing  deposits  to 
draw  interest  at  4$  from  the  first  day  of  every  quarter,  how 
much  will  be  due  him  Jan.  1,  1882  ? 

7.  Balance  the  following,  Jan.  1,  1884:  deposits  Jan.  1, 
1883,  $250  ;  Feb.  6,  $58  ;  Apr.  10,  $64.  Checked  out  March 
15,  $50 ;  May  13,  $75,  interest  beginning  from  the  first  of  each 
quarter. 

8.  What  would  be  due  a  depositor  at  the  end  of  the  year, 
who  had  a  balance  of  $563  in  bank  Jan.  1 ;  Jan.  8,  he  added 
$75  ;  March  28,  $65  ;  May  15,  $84 ;  Apr.  12,  withdrew  $15  ; 
Oct.  11,  $60,  int.  allowed  from  the  1st  of  the  month  following 
a  deposit  ? 

9.  The  balance  due  n  clerk  Jan.  1,  1882,  at  a  Savings  Bank 
was  $150 ;  April  1,  he  deposited  $75  ;  July  2,  $87  ;  and  Oct.  3, 
he  drew  out  $25;  how  touch  did  the  bank  owe  him  Jan.  1, 
1883,  interest  payable  semi-annually  "A 

«  .   V  * 

•kio.  Balance" the  following  pass-book  Jan.  1,  1883  : 
*  r,  . 
Dr.    Dime  Savings  Bank  in  acct.  with  J.  Hamilton.     Cr. 


Jan.     1 
Mar.  31 


Oct.      1 


Three  hundred  fifty  dollars 
One  hundred  twenty  dollars 
InJ.  to  July,  at  5%. 
Three  hun.  seventy-five  dol. 

Int.  to  January. 


Aug.    1  One  hundred  twenty  dollars 
Oct.    15  Sixty-five  dollars. 


Stocks 


506.  Stocks  represent  the  capital  or  property  of  incor- 
porated companies. 

507.  An  Incorporated  Company  is  an  association  authorized 
by  law  to  transact  business,  having  the  same  rights  and  obliga- 
tions as  a  single  individual. 

508.  The  capital  stock  of  a  company  is  divided  into  equal 
parts  called  Shares. 

Note. — The  par  value  of  a  share  varies  in  different  companies.  It  is 
usually  $100,  and  will  be  so  regarded  in  this  work,  uuless  otherwise 
stated. 

509.  A  Stock  Certificate  is  a  paper  issued  by  a  corporation, 
stating  the  number  of  shares  to  which  the  holder  is  entitled, 
and  the  par  value  of  each  share. 

510.  The  Par  Value  of  stock  is  the  sum  named  in  the 
certificate. 

511.  The  Market  Value  is  the  sum  for  which  it  sells. 

Notes. — 1.  When  shares  sell  for  their  nominal  value,  they  are  at  par; 
when  they  sell  for  more,  they  are  above  par,  or  at  &  premium;  when  they 
sell  for  less,  they  are  below  par,  or  at  a  discount. 

2.  When  stocks  sell  at  par  they  are  often  quoted  at  100  ;  when  at  1% 
above  par,  they  are  quoted  at  107,  or  at  1%  premium  ;  when  at  15%  below 
par,  they  are  quoted  at  85,  or  at  15  fc  discount. 

512.  A  Preferred  Stock  is  one  which  is  entitled  annually  to 
a  stated  per  cent  dividend  out  of  the  net  earnings,  before  the 
common  stock  dividend  is  declared,  and  may  be  cumulative  or 
not. 

Note. — When  cumulative,  if  the  earnings  are  not  sufficient  to  pay  the 
dividend  for  any  year,  the  holder  of  preferred  stock  is  entitled  to  the  back 
dividends  before  any  other  payments  are  made. 


Stocks  and  Bonds.  217 

513.  An  Installment  is  a  payment  of  part  of  the  capital. 

514.  An  Assessment  is  a  sum  required  of  stockholders  to 
replace  losses,  etc. 

515.  The  Gross  Earnings  of  a  company  are  its  entire 
receipts  from  its  ordinary  business. 

516.  The  Net  Earnings  are  the  remainder  after  all  expenses 
are  deducted. 

517.  A  Dividend  is  a  sum  divided  among  the  stockholders 
from  the  net  earnings  of  the  company. 

Note. — Companies  sometimes  declare  a  Scrip  Dividend,  entitling  the 
holder  to  the  sum  named,  payable  in  stock  at  par  value. 

518.  A  Bond  is  a  written  agreement  to  pay  a  sum  of  money, 
with  a  fixed  rate  of  interest,  at  or  before  a  specified  time.  The 
term  is  applied  to  National,  State,  city,  and  railroad  bonds,  etc. 

Notes. — 1.  Bonds  are  named  from  the  parties  who  issue  them,  the 
rate  of  interest  they  bear,  and  the  date  at  which  they  are  payable,  or 
from  all  united.  Thus,  "IT.  S.  4's  of  1907,"  means  that  these  bonds  bear 
4%  interest,  and  are  redeemable  after  1907,  at  the  pleasure  of  the 
Government. 

2.  Bonds  of  States,  cities,  corporations,  etc.,  are  named  by  combining 
the  rate  of  interest  they  bear  with  the  name  of  the  State,  corporation,  etc., 
by  which  they  are  issued  ;  as,  Ohio  G's,  N.  Y.  Central  5's,  etc. 

3.  Convertible  Bonds  are  those  which  may  be  exchanged  for  stock, 
lands,  or  other  property. 

519.  Bonds  are  also  known  as  first,  second,  etc.,  Mortgage 
bonds,  Income  bonds,  and  Consols. 

520.  A  Coupon  is  a  certificate  of  interest  due  on  a  bond,  to 
be  cut  off  when  paid,  as  a  receipt. 

Notes. — 1.  Income  bonds  are  those  on  which  interest  is  paid,  if  earned, 
and  are  not  usually  secured  by  a  mortgage. 

2.  The  term  "Consols"  is  applied  to  Bonds  issued  in  place  of  two  or 
more  classes  of  outstanding  bonds,  which  are  thus  consolidated  into  one 
class.     The  term  originated  in  England. 


218  Stocks  and  Bonds. 

521.  A  Mortgage  is  a  conveyance  of  real  estate  or  other 
property,  as  a  pledge  for  the  payment  of  a  certain  amount  of 
money. 

Note. — If  either  the  principal  or  interest  is  not  paid  when  due,  the 
mortgagee  has  a  right  to  take  or  sell  the  property. 


United    States    Bonds. 

522.  United  States  Bonds  are  known  as  Coupon  Bonds  and 
Registered  Bonds. 

523.  Coupon  Bonds  have  Interest  Certificates  or  Coupons 
attached  to  them,  and  are  negotiable  by  delivery.  For  this 
reason  they  sell  higher  in  foreign  markets  than  registered 
bonds. 

Registered  Bonds  are  those  payable  to  the  order  of  the 
owner,  whose  name  is  recorded  in  the  office  of  the  Register  of 
the  Treasury,  at  Washington,  D.  C.  They  can  be  transferred 
only  by  assignment  duly  acknowledged. 

Notes. — 1.  Letters  relating  to  the  transfer  of  registered  bonds  or  the 
payment  of  interest  on  the  same,  should  be  addressed  to  the  Register  of 
the  Treasury. 

2.  The  transfer  books  are  closed  for  30  days  previous  to  the  day  for 
the  payment  of  dividends  ;  and  stockholders  desiring  the  place  of  pay- 
ment changed,  must  give  notice  to  the  Register  one  month  at  least  before 
the  dividends  are  due. 

3.  When  bonds  are  sent  for  transfer,  state  where  the  interest  is  to  be 
paid,  inclose  the  stock  of  different  loans  in  separate  envelopes,  and  name 
on  each  the  amount  of  stock  and  the  date  of  the  Act  of  Congress  authoriz- 
ing its  issue. 

4.  Powers  of  Attorney  for  the  assignment  of  U.  S.  Bonds,  and  the 
assignments,  must  be  properly  filled,  before  transmission  to  the  Register. 

5.  Powers  of  Attorney  to  draw  interest  should  be  addressed  to  the 
First  Auditor  of  the  Treasury. 

6.  In  quotations  of  bonds,  the  accrued  interest  from  the  day  of  closing 
the  transfer  books,  is  included  in  the  price. 


Stocks  and  Bonds.  219 


NATIONAL    DEBT   OF   THE   UNITED   STATES. 

524.  The  National  Debt  of  the  United  States  is  divided 
into  Bonds,  Funded  Loads,  Refunding  Certificates,  Navy  Pen- 
sion Fund,  debt  bearing  no  interest,  etc.  No  nation  has  a 
common  name  for  all  its  debt. 

Funded    Debt    Bearing    Interest. 

Bonds  at  6%  continued  at  3 J $149,682,900.00 

"      at  b%        "  "     401,503,900.00 

"      at  4\% 250,000,000.00 

"      at  4^ 738,772,550.00 

Refunding  Certificates,  4% 575,250.00 

Navy  Pension  Fund,  3% 14,000,000.00 

$1,554,534,600.00 
Debt  bearing  no  Interest  since  maturity 11,528,265.26 

Non-Interest-bearing    Debt. 

Legal-tender  Notes $346,681,016.00 

Certificates  of  Deposit 9,590,000.00 

Gold  Certificates 5,188,120.00 

Silver         «         68,675,230.00 

Old  Demand  Notes 59,920.00 

Fractional  Currency 7,075,926.92        437,270,212.92 

Total  principal $2,003,333,078.18 

525.  Bonds  to  the  amount  of  $64,623,512,  known  as 
"Currency  Sixes,"  were  issued  to  the  Pacific  Railroads, 
and  the  interest  on  them  is  payable  by  the  United  States ; 
but  they  are  not  included  in  the  above  estimate,  as  the 
Government  holds  mortgages  on  the  roads  to  cover  the 
amount. 

Note. — These  took  their  name  from  the  fact  that  the  interest  on  them 
is  payable  in  currency  or  any  legal  tender.  All  United  States  Bonds  are 
exempt  from  taxation. 

526.  Of  the  funded  loans  there  are  registered  bonds  of  the 
various  issues,  in  denominations  of  $50,  $100,  $500,  $1000, 
$20000,  and  $50000  ;  and  coupon  bonds  of  $50,  $100,  $500, 
and  $1000. 


220  Stocks  and  Bonds. 


The  Funded  Debt  of  Foreign  Countries. 

527.  Consols  are  the  leading  funded  securities  of  the  Eng- 
lish Government ;  bearing  3%  interest,  payable  semi-annually. 
This  debt  amounted  in  1882  to  $3,814,500,000,  of  which 
$3,545,000,000  were  Consols,  or  Consolidated  Annuities,  re- 
deemable only  at  the  pleasure  of  the  Government. 

528.  The  funded  debt  of  France  bears  the  title  of  Rentes. 
The  rate  of  interest  is  usually  5%.  This  debt  in  1882  was 
$4,750,337,109.  Besides  this  the  "Bons  du  tresor"  amount 
to  $65,000,000. 

529.  The  German  Empire  has  only  about  $70,000,000 
funded  debt  bearing  4%  interest,  known  as  4%  Imperial  bonds. 

530.  In  1882  Austria  had  a  funded  debt  of  $1,450,000,000, 
the  larger  part  bearing  b%  interest,  known  as  "Austrian  Consols." 

531.  Russia  had  a  debt  of  $2,421,417,932,  a  portion  of 
which  bears  a  nominal  interest  of  5  and  5|$.  They  are 
known  as  Oriental  loans,  and  are  below  par. 

Prussia  has  a  debt  of  $498,500,000,  of  which  $220,000,000 
is  consolidated  (zuheilung)  at  an  average  of  4%  interest. 

Italy  has  an  immense  debt,  of  which  $380,000,000  are  in 
"  Rentes  "  of  3  and  5  per  cent. 

STOCK     EXCHANGES. 

532.  Stock  Exchanges  are  Associations  organized  for  buying 
and  selling  stocks  and  bonds  and  other  similar  securities. 

533.  Members  are  elected  by  ballot.  The  qualifications  for 
membership  are  good  character  and  solvency. 

534.  The  Officers  are  a  President,  Vice-President,  Treasurer, 
Clerk,  Secretary,  Standing  Committee,  Finance  Committee, 
Committee  on  Listing  Stocks,  and  a  Nominating  Committee. 

Notes. — 1.  Every  Association  makes  its  own  By-Laws,  which  are 
stringent  and  rigidly  enforced. 


The  Stock  Exchange.  221 

2.  A  system  of  Arbitration  supersedes  all  appeals  to  the  law  for  the 
settlement  of  disputes. 

535.  The  New  York  Stock  Exchange  is  composed  of  1200 
members,  the  maximum  allowed  by  their  By-Laws.  It  is  said 
that  seats  at  this  Board  have  recently  been  sold  at  prices  rang- 
ing from  $20,000  to  $30,000. 

536.  The  Exchange  is  open  for  business  from  10  a.m.  to 
3  p.  m.  Before  any  new  securities  are  allowed  to  be  quoted  or 
sold  on  the  Exchange,  they  are  subjected  to  a  rigid  examina- 
tion by  the  Committee  on  "Listing"  Stocks. 

537.  There  are  two  lists  of  Stocks,  one  is  known  as  the 
Regular  list,  the  other  as  the  Free  list. 

538.  Ordinarily  Stocks  and  Bonds  are  quoted  at  a  certain 
per  cent  on  the  par  value  of  $100  per  share.  Stocks  of  the 
par  value  of  $50  are  called  half  stocks,  and  those  whose  par 
value  is  $25  are  called  quarter  stocks,  and  the  price  quoted 
is  the  percentage  of  the  par  value. 

The  commission  for  buying  or  selling  Stocks  or  U.  S. 
Bonds  is  |  of  1%  (i%). 

Mining  Stocks  are  quoted  at  so  much  per  share,  and  the 
commission  varies  according  to  the  price  of  the  stock. 

539.  Pipe-line  certificates  are  quoted  at  so  much  per  bbl.  for 
1000  bbl.  of  crude  Petroleum  oil. 

540.  Stocks  sold  "  regular  way  "  are  paid  for  and  delivered 
on  the  next  business  day.  On  sales  made  "  buyer  three "  or 
"  seller  three  "  no  interest  is  charged  ;  on  contracts  longer  than  3 
days,  the  buyer  pays  interest,  unless  otherwise  specified.  ~No 
contracts  for  more  than  60  days  are  recognized. 

Notes. — 1.  "Seller  3,"  means  deliverable  on  either  of  3  d.,  at  the 
option  of  the  seller.  "Buyer  3,"  means  the  buyer  can  demand  delivery 
within  3  d.,  but  must  take  and  pay  for  it  the  third  day. 

2.  Quotations  are  termed  "flat"  when  the  accrued  interest  is  included 
in  the  price  named. 


222  Stocks  and  Bonds. 

541.  Margin  is  cash  or,  other  security  deposited  with  a 
broker  on  account  of  either  the  purchase  or  sale  of  securities, 
and  to  protect  him  against  loss  in  case  the  market  price  of  the 
securities  bought  or  sold  varies  so  as  to  be  against  the  interests 
of  the  customer.  It  is  usually  10$  of  the  par  value  of  the 
stock. 

Note. — Brokers  charge  interest  on  the  sums  expended  and  allow 
interest  on  the  margins  deposited. 

542.  A  Bear  is  an  operator  who  believes  the  market  price  of 
stocks  will  fall 

543.  A  Bull  is  an  operator  who  believes  the  market  price 
of  stocks  will  advance. 

Note. — Hence  a  bull  will  buy  stocks  in  order  to  profit  by  the  I  i /her 
price  at  which  he  expects  to  sell,  and  a  bear  will  sell  in  order  to  profit  by 
the  lower  price  at  which  he  expects  to  buy. 

544.  Hypothecating  stocks  and  bonds  is  depositing  them 
as  collateral  security  for  money  borrowed. 

Note. — The  securities  must  be  greater  than  the  loan  by  at  least  10% 
of  their  par  value,  and  in  every  case  by  an  amount  equal  to  20%  of  the 
amount  of  the  loan.     This  excess  is  called  the  margin  of  the  loan.. 

545.  Watering  Stock  is  increasing  the  number  of  shares  of 
an  incorporated  company  without  a  corresponding  increase  in 
their  value. 

546.  A  Corner  is  produced  when  one  or  more  operators 
owning  or  controlling,  all  the  stock  of  a  company  are  able  to 
purchase  still  more  for  either  immediate  or  future  delivery. 
When  they  demand  the  stock,  the  sellers  are  unable  to  find 
it  in  the  market. 

547.  A  Syndicate  is  a  combination  of  Brokers,  Bankers,  or 
Capitalists  who  undertake  to  place  large  loans,  and  transact 
other  business. 

Note.— Stock  Privileges  known  as  "  Puts."  "  Calls,"  "  Spreads,"  and 
"  Straddles,"  are  not  recognized  by  the  Stock  Exchange, 


Stock  Investments.  223 


Quotations    in    Stocks. 

548.  The  following  are  taken  from  a  report  of  sales  at  the 
New  York  Stock  Exchange  in  Dec,  1883.  The  abbreviations 
which  appear  will  be  explained  hereafter  in  the  Appendix. 

10000  4's,  coup 123£  I  Cen.  Pac.  1.  g 104i  @  104£ 

50000  4's,  reg 122|    Erie,  5th 105 


800003's,  "    101 

25000  4£V  114J 

2000  N.  C.  4's,  en 81} 

1000  Tenn.  f.  new  S 38 

10  sh.  Am.  Ex.  Bank 130 

100  Chi.  &  N.  W.  pf 142} 

100  Mut.  Un.  s.  f.  6's 84£ 


Cur.  6's,'95 127i 

Chi.  Bur.  &  Q.  5's  Deb 91| 

N.  Y.  Central 116  @  116| 

N.  Y.  Elevated 105 

Chi.  &  W.  Ind.  s.  f 106.| 

N.J.  Central 83  £ 

Va.  Mid.  inc 63| 


Seller's    Option. 


500  Sh.  N.  Y.  EL  ©  105,  S.  60.  New  YorK)  Dec.  15>  1883> 

I  have  Purchased  of  Lockwood  Bros.  Five  Hundred 
(500)  Shares  of  the  Capital  Stock  of  the  Netv  York  Elevated 
Railroad  Company,  at  one  hundred  five  dollars  ($105)  per  share; 
payable  and  deliverable  at  seller's  option  within  sixty  (60) 
days  ivith  interest  at  the  rate  of  6%  per  annum. 

H.  B.  Stevenson. 
Buyers    Option. 


500  Shares  N.  Y.  0.  @  116,  B.  30.      New  York>  Dec.  28>  1883. 

/  have  Sold  to  E.  J.  Marshall  Five  Hundred  (500) 
Shares  of  the  Capital  Stock  of  the  Neio  York  Central  Railroad 
Company,  at  one  hundred  sixteen  per  cent;  payable  and 
deliverable  at  buyer's  option  within  thirty  (30)  days  with 
interest,  at  the  rate  of  six  (6)  per  cent  per  annum. 

C.  B.  Hatch. 

STOCK    INVESTMENTS. 

549.  Premiums,  Discounts,  Dividends,  and  Assessments, 
are  computed  by  Percentage. 

The  par  value  of  the  stock  is  the  Base ;  the  per  cent  of 
premium,  dividend,  or  discount  is  the  Rate;  the  premium, 
discount,  or  dividend  is  the  Percentage. 


224  Stocks  and  Bonds. 

550.  To  find  the  Cost  of  stock,  the  par  value  and  the  rate  of 
premium,  discount  or  dividend  being  given. 

1.  What  cost  50  shares  R.  R.  Stock,  at  6%  premium,  par 
value  1100,  brokerage  \%  ? 

Analysis. — The  cost  of  1  share,  at  6  %  premium  +  \  %  brokerage  = 
$106,125.    Cost  of  50  shares  =  $106,125  x  50  =  $5306.250,  Ana. 

2.  What  cost  60  shares  of  R.  R.  Stock,  at  8%  discount, 
brokerage  \%  ? 

Analysis. — The  cost  of  1  share,  at  8%  discount,  and  \%  brokerage  = 
$92,125.     Cost  of  60  shares  =  $92,125  x  60  =  $5527.50,  Ans.     Hence,  the 

Rule. — Multiply  the  cost  of  1  share  by  the  number  of 
shares. 

Note. — In  finding  the  entire  cost  of  stocks  the  rate  %  of  brokerage  is 
added  to  the  rate  above  or  below  par,  as  both  are  calculated  on  the  same 
amount.     (Art.  538.) 

3.  What  must  be  paid  for  800  shares  Telegraph  stock,  at 
25$  premium,  brokerage  \%  ? 

4.  What  are  60  shares  Erie  R.  R.  stock  worth,  at  15J<£ 
discount? 

5.  What  must  be  paid  for  U.  S.  bonds,  par  value  $5000,  at 
106,  brokerage  \%  on  the  par  value  ? 

Solution.— 50  shares,  at  106  =  $5300,  and  {\%  brokerage)  $6.25  = 
$5306.25. 

6.  What  cost  75  shares  Union  bank  stock,  at  8f%  premium, 
brokerage  \%  ? 

7.  The  premium  on  stocks  sold  was  $858,  the  par  value 
$7550 ;  what  was  the  cost  ? 

8.  The  discount  on  a  Mining  stock  is  15j%  par  value  $50; 
what  is  the  value  of  23  shares  ? 

551.  To  find  the  premium,  discount,  dividend,  or  assessment, 
the  number  of  shares  and  rate  being  given. 

9.  What  would  a  stockholder  of  New  York  and  New  Haven 
R.  R  Co.  receive,  who  owns  500  shares,  from  a  4=%  dividend? 


Stock  Investments.  225 

Solution.— 500  shares  at  $100  =  $50000  tlie  par  value, 
$50000  x  .04  =  $2000.00,  Ans.     Hence,  the 

Rule. — Multiply  the  par  value  of  stoelc  by  the  rate  %. 

10.  A  western  R.  R.  Co.  called  for  an  assessment  of  12\% ; 
how  much  must  a  man  pay  who  owns  350  shares  ? 

11.  The  stock  of  a  mining  Co.  was  sold  at  a  discount  of  4$$; 
how  much  was  received  for  800  shares,  par  value  $50  a  share  ? 

552.  To  find  the  Rate  %,  the  par  value  of  stock,  the  premium, 
discount,  dividend  or  assessment  being  given. 

12.  The  capital  stock  of  a  Co.  was  $100000,  the  dividend 
$22000;  what  was  the  rate  per  cent? 

Solution.— $22000.00  -*-  $100000  =  .22,  or  22%,  Ans.    Hence,  the 

Rule. — Divide  the  premium,  discount,  assessment,  or 
dividend,  by  the  par  value  of  the  stoelc. 

13.  The  discount  on  75  shares  Panama  R.  R.  stock  was 
#725  ;  what  %  was  it  ? 

14.  A  man  owning  25  shares  Western  Union,  was  assessed 
$85  ;  what  was  the  rate  per  cent  ? 

553.  To  find  the  number  of  shares,  when  the  sum  invested  and 
the  cost  of  I  share  are  given. 

15.  How  many  shares  of  factory  stock  at  6%  discount  and 
brokerage  \%,  can  be  bought  for  $76200  ? 

Analysis. — Since  the  discount  is  5%  and  brokerage  }%,  the  cost  of  1 
share  is  95%+£%,.or  95J%  of  $100  =  $95.25.  As  $95.25  will  buy  1 
share,  $76200  will  buy  as  many  shares  as  $95.25  are  contained  times  in 
$76200,  and  $76200  -j-  $95.25  =  800  shares,  Ans.     Hence,  the 

Rule. — Divide  the  sum  invested  by  the  cost  of  one 
share. 

16.  How  many  shares  of  Mutual  Union  telegraph  stock,  at 
15$%  discount  and  brokerage  \%,  can  you  buy  for  $13500  ? 


226  Stocks  and  Bonds. 

17.  Find  the  number  of  pipe  line  certificates  at  115J,  that 
can  be  bought  for  $15150,  brokerage  \%. 

18.  What  number  of  elevated  railroad  shares  at  105, 
brokerage  \%,  will  $75150  pay  for? 

19.  Find  the  number  of  shares  of  Union  Pacific,  at  20% 
discount,  that  can  be  bought  for  $32000  ? 

554.  To  find  how  stock  must  be  bought  which  pays  a  given  per 
cent  dividend,  to  realize  a  specified  per  cent  on  the  investment. 

20.  At  what  price  must  I  buy  stock  which  pays  6%  dividend, 
so  as  to  realize  8%  on  the  investment? 

Analysis. — Since  the  annual  income  of  $1  is  .06,  this  must  be  Tf^  of 
the  price  to  be  paid;  then  -^  =  .06  -*-  .08  =  $.  75,  and  £{$  =  $75. 
Hence,  the 

Kule. — Divide  the  rate  which  the  stock  pays  by  the 
required  rate,  the  quotient  will  be  the  price  of  $1  stock. 

21.  What  must  be  paid  for  U.  S.  4's  that  8%  may  be  received 
on  the  investment  ? 

22.  What  must  be  paid  for  stock  that  yields  20%  dividends, 
so  as  to  realize  1\%  on  the  investment  ? 

555.  To  find  what  sum  must  be  invested  to  yield  a  given 
income,  when  the  market  value,  and  the  rate  of  interest  are  given. 

23.  What  sum  must  be  invested  in  N.  Y.  5's,  at  108£,  to 
produce  an  annual  income  of  $2500  ? 

Analysis. — The  income  $2500 -j- $5  (int.  on  1  share)  =  500  shares,  and 
108^  (price  of  1  share)  x  500  =  $54250.    Hence,  the 

Kule. — Multiply  the  market  value  of  1  share  by  the 
number  of  shares. 

24.  How  much  must  be  invested  in  U.  S.  4's,  at  123§,  to 
yield  $3500  annually? 

25.  What  must  be  invested  in  Nebraska  8's,  at  75,  to  yield 
an  income  of  $3540  annually  ? 


Stock  Investments.  227 

26.  What  sum  must  be  invested  in  stock  at  112,  which  pays 
10%  annually,  to  obtain  an  income  of  $3200  ? 

27.  How  much  must  be  invested  in  Alabama  6's,  at  85,  to 
realize  $2500  a  year  ? 

28.  How  much  must  be  invested  in  stock  at  106,  to  yield  an 
income  of  $6000,  the  stock  paying  10%  dividend  annually  ? 

556.  To  find  the  %  of  income  from  a  given  investment,  without 
regard  to  its  maturity. 

29.  What  is  the  %  income  on  bonds  bought  at  125,  paying 
1%%  interest  ? 

Analysis. — Since  the  int.  on  1  share  ($100)  is  $12,  the  int.  on  $125  is 
fa  of  $12,  and  $12-s-$125  =  .09?,  or  9f#,  Ana. 

30.  Bought  5%  bonds  at  75  ;  what  will  be  the  %  income  ? 
Solution.— $5^-75  =  .06|,  or  6|%,  Ana.     Hence,  the 

Rule. — Divide  the  income  per  share  by  the  cost  per 
share. 

31.  Find  the  per  cent  of  income  on  U.  S.  4}'s,  bought  at 

tut 

32.  What  is  the  per  cent  of  income  on  Iowa  6's,  bought  at 
108},  brokerage  \%  ? 

33.  Which  is  the  more  profitable,  $10000  invested  in  3  per 
cents  at  101,  or  in  4  per  cents  at  122}? 

34.  If  a  person  were  to  transfer  $29000  stock  from  3}  per 
cents  at  99  to  3  per  cents  at  90-|  what  would  be  the  difference 
in  his  income  ? 

35.  A  man  agreed  to  take  300  shares  of  mining  stock,  par 
value  $50  ;  after  the  third  installment  was  paid  amounting  to 
75^  of  the  par  value,  a  dividend  of  3%  was  declared  ;  how 
much  and  what  %  on  the  actual  cost  did  he  receive  ? 


228  Stocks  and  Bonds. 

557.  To  find  the  %  income  from  a  given  investment  payable  in 
a  given  time. 

36.  What  per  cent  income  will  be  received  if  I  buy  U.  S.  4's 
at  112,  payable  at  par  in  16  years? 

Analysis — Since  the  bond  matures  in  16  years,  the  premium  on  1  share 
($12)  decreases  j-f,  or  $|  each  year.  The  int.  $4— $f  =  $3£  income.  And 
$3.25-r-$112  (cost  of  1  share)  =  ^\\\°/c  the  rate  required. 

37.  Bought  Tennessee  bonds  at  38,  bearing  ±%  int.,  having  25 
years  to  run  ;  what  per  cent  will  be  realized  if  they  are  paid  at 
par  at  maturity  ? 

38.  What  per  cent  income  will  be  gained  from  S%  bonds, 
bought  at  90,  and  payable  at  par  in  20  years  ? 

Analysis. — Since  the  maturity  is  20  years,  the  discount  ($10)  decreases 
£&,  or  $|  each  year.  The  int.  $8  +  -|  =  $8£  income  ;  and  $8.50h-$90  = 
$.09,*,  or  9|%  the  required  rate.     Hence,  the 

Rule. — First  find  the  average  annual  decrease  of  the 
premium  or  discount. 

If  the  bonds  are  at  a  premium,  subtract  it  from  the 
given  rate  of  interest;  if  at  a  discount,  add  it  to  the 
interest ;  the  result  will  be  the  average  income  of  one 
share. 

Divide  the  average  income  of  one  share  by  the  cost  of 
one  share,  and  the  quotient  will  be  the  rate  per  cent  of 
income. 

Notes. — 1.  When  bonds  are  at  a  premium,  the  longer  the  time  before 
maturity,  the  greater  will  be  the  rate  per  cent  of  income. 

2.  "When  bonds  are  at  a  discount,  the  longer  the  time  before  maturity, 
the  less  will  be  the  rate  per  cent  of  income. 

39.  What  rate  per  cent  of  income  will  be  received  on  IT.  S. 
4J's  at  114,  payable  at  par  in  16  years? 

40.  Bought  Kentucky  bonds  at  90,  due  at  par  in  30  years, 
drawing  8%  interest ;  what  is  the  per  cent  of  income  ? 

41.  In  1882  Milwaukee  and  St.  Paul  6'§,  due  at  par  in  1930, 
were  bought  for  108  ;  what  interest  will  this  pay  ? 


/Stock  Investments.  229 

Note. — Other  methods  of  analysis  than  those  given  are  often  used  by 
dealers  in  stocks  and  bonds.  Take  Ex.  41.  The  amt.  of  $100  (1  share)  at 
6%  for  48  years  equals  $388.  Subtracting  cost,  $388— $108  =  $280,  total 
income.  The  question  now  becomes,  "  What  per  cent  of  $108  will  yield 
$280  in  48  years?"  In  1  year,  1%  of  $108  =  $1.08,  and  in  48  years 
$1.08  x  48  =  $51.84.  If  $51.84  =  1  % ,  $280  =  as  many  %  as  $51.84  are 
contained  times  in  $280,  or  §^  % . 


42.  If  I  pay  108  for  U.  S.  4's,  having  15  years  to  run,  what 
%  will  I  receive  if  I  keep  them  till  they  mature  and  they  are 
paid  at  par  ? 


558.  To  find  how  stock  must  be  bought  which  has  several 
years  to  run,  and  pays  a  given  %  dividend,  to  realize  a  specified 
per  cent  on  the  investment. 

43.  At  what  price  must  6%  bonds,  payable  in  8  years,  be 
bought  to  realize  4=%  on  the  investment. 

Analysis.— The  Amt.  of  $100,  at  6%  in  8  yrs.  =  $148. 
The  Amount  of  $1,  at  4%  in  8  yrs.  =  $1.32. 
$148-s-$1.32  =  $112j&  per  share.     Hence,  the 

Rule. — Find  the  amount  of  $100  for  the  given  time 
and  rate,  and  divide  it  by  the  amount  of  $1  for  the 
same  time,  at  the  rate  required. 

44.  Bought  railroad  6%  bonds  payable  in  5  years,  and  expect 
to  realize  11%  on  the  investment ;  what  did  I  pay  ? 

45.  What  must  I  pay  for  5  per  cent  bonds,  which  mature  in 
15  years,  that  my  investment  may  yield  4  per  cent  ? 

46.  What  shall  I  pay  for  a  bond  of  $500,  having  12  years  to 
run,  with  interest  at  6%,  in  order  to  make  it  an  8%  invest- 
ment? 

Practical    Examples. 

559.  l.  At  what  price  must  a  stock  paying  semi-annual 
dividends  of  2%  be  bought,  to  yield  6%  per  annum  on  the 
capital  invested  ? 

2.  If  the  semi-annual  dividends  are  2\%,  how  must  the 
stock  be  bought  to  yield  5%  ? 


230  Stocks  and  Bonds. 

3.  Which  is  the  more  profitable  investment,  a  stock  at  120, 
paying  8%  annually,  or  a  20-year  bond  at  90,  paying  6%  annually  ? 

4.  Three  companies,  A,  B,  and  C,  are  to  be  consolidated  on 
the  basis  of  the  relative  market  values  of  their  stock. 

Thus,  A's  capital  $1,000,000,  Market  value  100%; 
B's      "       $1,500,000,       "  "       50%; 

C's       "  $625,000,       "  "       40%. 

The  capital  of  the  consolidated  company  is  to  be  $2,000,000, 
in  20000  shares  of  $100  each.  What  proportion  and  what 
amount  of  the  capital  should  be  allotted  to  each  of  the  old 
companies ;  and  how  much  stock  in  the  new  company  should 
the  holder  of  1  share  of  the  stock  of  each  of  the  old  companies 
be  entitled  to  ? 

5.  When  3%  government  bonds  are  quoted  at  101,  what  sum 
must  be  invested  to  yield  an  income  of  $800  a  year  ? 

6.  What  is  the  accurate  interest  on  an  investment  of  $5000 
in  U.  S.  4£'s  at  114J,  from  Jan.  1  to  March  1,  inclusive  ? 

7.  If  a  man  buys  stock  at  17%  above  par,  what  per  cent  does 
he  receive  on  his  investment,  if  the  stock  pays  a  dividend  of 
8\%  on  its  par  value  ($100)  ? 

8.  A  man  bought  8  shares  of  stock  at  108|,  and  after  keep- 
ing it  11  months  received  a  dividend  of  $7  a  share,  and  sold 
the  stock  then  at  109£ ;  what  per  cent  did  he  receive  on  his 
investment  ? 

9.  How  many  shares  of  Mutual  Union  Telegraph  stock  at 
84J,  can  be  bought  for  $12000,  brokerage  \%  ? 

10.  Bought  Oct.  12th,  400  Pacific  Mail  at  42J,  and  200  Mich. 
Cen.  at  92 £;  Nov.  10  sold  the  former  at  42 J,  and  the  latter  at 
92| ;  what  was  my  gain  ? 

n.  Which  would  be  the  better  investment,  $12120  in  N.  J. 
Central  at  84,  paving  3%  annual  dividends,  or  the  same  invested 
in  Chemical  Bank  stock  at  2020,  paying  15%  every  2  months? 

12.  A  customer  deposited  $500  margin  with  a  broker 
Nov.  23,  who  purchased  for  him  50  shares  Mich.  Central  at  80. 
He  sold  the  same  stock  Nov.  30th  at  98 ;  what  was  the  gain, 
brokerage  \%  ? 


Stock  Investments. 


231 


OPERATION. 


Dr. 


Nov.  23. 


To  50  sh.  Mich.  Cen.  at  80. .  $4000 

Brokerage  \% 6.25 

Nov.  30.    Int.  on  $4006.25,  7  days 

fa 

By  margin  deposited 


Nov.  23. 
•*     30. 

Nov.  30. 
Note 


By  50  sh.  Mich.  Cen.  at  98. .  $4900 
Less  Brokerage  |  %  . . . .  6.25 

Int.  on  $500,  7  days 

—The  brokerage,  £  of  1%  is  equal  to 
$12.50  on  100  shares  of  stock  at  the  par  value  of 
$100  each. 


4006 

25 

4 

67 

4010 

500 

4893 

75 

0 

58 

5394 
$1383 

Balance 

Less  margin 

500 

Gain. . 

$883 

92 


13.  A  man  bought  100  shares  Union  Pacific  at  79},  and  sold 
the  same  at  82f  ;  what  was  the  gain,  less  \%  brokerage  ? 

14.  Governments  yielding  $240  a  year  at  4$  interest,  were 
sold  at  108,  and  the  proceeds  invested  in  land  at  $75  an  acre  ; 
how  many  acres  were  bought  ? 

15.  What  cost  25  shares  of  111.  Cent,  at  a  premium  of  33$  ? 

16.  What  rate  of  dividend  on  the  above  would  be  equal  to 
6$  interest  on  the  investment  ?• 

17.  If  the  N.  Y.  Cen.  declares  a  dividend  of  15$,  how  much 
will  a  man  receive  who  owns  250  shares  ? 

18.  What  per  cent  on  his  investment  if  he  bought  the  above 
stock  at  95  ?     What  per  cent  if  bought  at  116  ? 

19.  Which  is  the  better  investment,  R.  R.  stock  at  25$ 
discount,  and  paying  a  semi-annual  dividend  of  4$,  or  money 
loaned  at  10$,  interest  payable  annually  ?    What  %  better  ? 

20.  If  the  annual  dividend  on  a  stock  is  15$  and  money  is 
loaned  at  10$  per  annum,  what  should  be  the  price  of  the  stock? 

21.  On  84  shares  of  stock  2  semi-annual  dividends  were 
declared,  one  at  5$,  the  other  at  4$,  the  investment  paid  10$; 
what  did  the  stock  cost  ? 

22.  A  man's  income  from  $2000  worth  of  stock  is  $75  semi- 
annually ;  what  is  the  per  cent  per  annum  ? 


232  Produce  Exchanges. 

23.  At  what  per  cent  discount  must  6%  stock  be  bought, 
that  the  investment  may  pay  9%  ? 

24.  If  a  stock  yields  15$  per  annum,  what  is  its  value  when 
money  is  worth  8%  ? 

25.  March  4th,  deposited  with  my  broker  $500  margin, 
for  purchasing  50  shares  Mo.  Pacific  K.  R.  stock  at  92J.  The 
stock  was  sold  March  28th  at  96f .  Allowing  6%  interest  on 
the  deposit,  and  charging  6%  interest  on  the  purchase,  and  \% 
brokerage,  what  was  the  net  profit  on  the  transaction  ? 

26.  Sold  "short"  through  my  broker  200  shares  Mich. 
Cent,  at  90,  and  "covered"  my  "short"  at  86|.  Allowing  \% 
commission  for  buying  and  selling,  what  was  my  net  profit  ? 

27.  What  rate  per  cent  income  will  be  received  on  U.  S.  4's 
at  108,  payable  at  par  in  15  years  ? 

28.  A  man's  income  from  U.  S.  4's  of  1907,  bought  at  123, 
and  3's  at  101,  is  $350.  If  bought  at  par  an  equal  sum  would 
have  been  invested  in  each ;  how  much  was  his  investment  ? 
How  many  shares  of  each  stock  did  he  buy  ? 

29.  Paid  86}  for  stock  bearing  8%  annual  dividends ;  and 
received  each  year  $480  ;  what  was  the  investment  ? 

30.  Borrowed  $100000  upon  1000  shares  N.  Y.  Cent,  at  120. 
If  the  market  price  falls  to  par,  how  much  more  of  the  same 
stock  must  I  deposit  with  the  lender  to  keep  up  the  original 
margin  ?     (Art.  544,  N.) 

PRODUCE    EXCHANGES. 

560.  Produce  Exchanges,  or  Boards  of  Trade,  are  Associa- 
tions of  dealers  in  Produce.  They  make  their  own  By-Laws 
and  are  conducted  by  a  Board  of  Directors,  usually  including 
a  President,  Vice-President,  Secretary,  and  Treasurer,  who  are 
elected  by  ballot. 

The  fee  for  membership  is  $1000  and  upwards.  They  have 
committees  on  Complaints,  Arbitration,  Appeals,  Trades,  Prices, 
Transportation,  Information  and  Statistics,  etc. 


Produce  Exchanges.  233 

561.  The  department  which  most  concerns  the  public,  is  the 
Inspection  by  their  committees  of  the  great  staples  of  food,  as 
grain,  flour,  the  various  kinds  of  provisions,  peas,  beans,  beef, 
pork,  lard,  butter,  cheese,  eggs,  and  all  the  important  products 
of  the  country. 

To  protect  the  public  against  fraud  and  adulterations,  they 
classify  these  various  articles  according  to  quality,  after  careful 
inspection,  and  adopt  marks  or  brands  for  each,  by  which  they 
become  known  in  the  markets  of  the  world. 

What  the  Stock  Exchange  is  to  financial  securities,  the 
Produce  Exchange  is  designed  to  be  to  the  staples  of  food. 

Note. — Exchanges  have  already  become  important  accessories  of 
commerce.  They  facilitate  speculation  as  well  as  regulate  it ;  they  are 
courts  of  arbitration  for  settling  disputes,  and  are  considered  almost  a 
necessity  to  the  interests  they  represent.  Many  associations  have 
mutual  life  insurance  attachments  connected  with  them.  In  addition  to 
the  stock  and  produce  exchanges  there  are  Real  Estate,  Petroleum,  Cotton, 
Tea,  Coffee  Exchanges,  etc.,  each  with  a  separate  organization,  the 
avowed  objects  of  which  are  to  advance  the  interests  of  trade  and 
commerce. 

1.  What  %  do  I  make  by  purchasing  flour  at  $7.50  per  barrel 
cash  and  selling  it  for  $8.25  on  3  mo.  credit,  when  money  is 
worth  6%  ? 

2.  A  man  has  a  bin  28  ft.  long,  5  ft.  4  in.  wide,  and  4  ft. 
deep,  filled  with  wheat ;  what  is  it  worth  at  $1.15  per  bushel? 

Note. — The  quantity  of  grain  in  bins,  etc:,  is  found  by  reducing  it  to 
cubic  inches  and  dividing  the  result  by  the  number  of  cubic  inches  in  a 
bushel.     (Art.  71.) 

3.  A  dealer  has  3  bins  of  wheat  containing  700,  950,  and 
1000  bu.  respectively ;  he  has  sold  3  lots  of  400  bu.,  1  lot  of 
75  bu.  1  pk.  5  qt.,  and  6  lots  each  of  10  bu.  3  pk.  2  qt. ;  what  is 
the  value  of  what  he  has  left  at  $1.15  per  bushel? 

4.  Bought  wheat  at  $1.10  a  bushel,  allowing  \\%  for  waste 
and  2  cts.  a  bu.  for  storage;  how  must  it  be  sold  to  gain  8%? 

5.  The  net  proceeds  of  a  shipment  of  hay,  sold  at  $28  per 
ton,  were  $12580  after  deducting  3%  commission  and  $500  for 
other  charges;  how  many  tons  of  hay  were  shipped  ? 


234  Storage. 

6.  A  dealer  received  10000  barrels  of  flour  to  sell  on  com- 
mission, and  was  to  invest  the  proceeds  in  TJ.  S.  notes  at  Y^% 
interest;  he  paid  $759  charges,  sold  the  flour  at $9  a  barrel  and 
charged  3%  commission  on  the  sales ;  what  amount  of  notes 
could  he  buy  at  36%  premium,  brokerage  \%  ? 

7.  A  produce  merchant  bought  30000  bu.  corn  at  $0.55, 
paying  $450  charges,  and  $225  storage ;  he  sold  it  at  25$ 
advance  on  the  entire  cost  on  90  days  time  ;  at  what  price  per 
bu.  did  he  sell  it,  and  what  per  cent  did  he  gain  at  the  time  of 
sale,  money  being  7%  interest  ? 

8.  The  net  proceeds  of  a  sale  of  1000  tons  of  hay  at  $20  per 
ton  were  $18325,  after  deducting  $875  for  charges;  what  was 
the  rate  %  of  commission  ? 

9.  A  dealer  expended  equal  sums  in  wheat,  rye,  and  oats ; 
on  selling  he  made  H%  on  the  wheat,  b%  on  rye,  and  lost  15$ 
on  the  oats  ;  the  whole  sum  received  was  $1782 ;  what  sum  did 
he  invest  in  each  kind  of  grain  ? 

10.  A  grain  merchant  bought  9000  bu.  wheat,  paying  at  his 
option  $1  cash  per  bu.,  or  $1.10  on  3  mo.;  which  would  be  the 
more  advantageous,  to  buy  on  credit,  or  to  borrow  the  money  at 
7%  and  pay  cash  ? 

STORAGE. 

562.  The  business  of  Storage  is  done  by  commission  and 
forwarding  merchants.  The  prices  charged  are  regulated  by 
the  Board  of  Trade  of  the  city  in  which  the  Storage  is  made, 
unless  by  a  special  agreement. 

563.  The  rates  are  usually  fixed  at  a  certain  price  per  barrel, 
bushel,  box,  bale,  etc.,  for  one  month  of  30  days. 

Notes. — 1.  In  some  cities  a  full  month's  storage  is  charged  for  any  part 
of  a  month  they  may  remain  in  store,  in  others  15  days  or  less  are  called 
|  mo.  and  over  15  days  a  whole  month. 

2.  On  Grain  the  charge  per  bushel  for  storage  varies  in  different 
cities. 


Storage. 


235 


564.  Accounts  of  Storage  ordinarily  contain  an  entry  of 
articles  received  and  delivered  with  the  date  of  each.  They  are 
somewhat  similar  to  bank  accounts. 

565.  To  Average  a  Storage  Acct.  according  to  actual  time. 

l.  Received  on  storage  and  delivered  the  following :  May  1, 
1883,  1000  bbl.  flour;  May  26,  2000  bbl.  Delivered,  May  16, 
500  bbl.;  June  1,  1000  bbl.;  June  12,  1100  bbl.;  July  2,  400 
bbl. ;  what  was  the  cost  of  storage  at  6  cts.  a  mo.  per  barrel  ? 

Acct.  of  Storage  of  flour  received  and   delivered  for  acct.  of 
A.  Hamilton  of  Chicago. 


Date. 

Received. 

Delivered. 

Balances. 

Days. 

Products. 

1883. 

May     1 

1000  bbl. 

1000  bbl. 

15 

15000 

"      16 

500  bbl. 

500   " 

10 

5000 

"      26 

2000    " 

2500   " 

5 

12500 

June    1 

1000   " 

1500   " 

11 

16500 

"      12 

1100   " 

400   " 

20 

8000 

July    2 

400   « 

000   " 

00 

0000 

3000  bbl. 

3000  bbl. 

30 ) 57000 

Storage  for  1  month  for  1900  bbl. 
1900  x. 06  =$114.00,  Ans. 

Rule. — Multiply  the  number  of  barrels,  etc.,  by  the 
number  of  days  they  are  in  store  between  the  time  of 
entrance  and  delivery.  Multiply  each  balance  by  the 
number  of  days  it  remains  unchanged.  Divide  the  sum 
of  products  by  SO,  the  quotient  is  the  number  of  articles 
in  store  for  one  month. 

2.  Received  and  delivered  on  account  of  Samuel  Barrett  of 
New  Orleans  sundry  bales  of  cotton  as  follows:  Received 
Jan.  1, 1884,  2310  bales  ;  Jan.  16,  120  bales  ;  Feb.  1,  500  bales; 
Feb.  12,  200  bales.  Delivered  Feb.  12,  1200  bales ;  March  6, 
800  bales  ;  April  3,  400  bales  ;  April  10,  300  bales.  Balance 
the  account  to  May  1,  and  find  the  storage  due  at  15  cents  a 
bale  per  month. 


236  Life  Insurance, 

3.  Eeceived  on  storage,  and  delivered  the  following  merchan- 
dise :  Received  Jan.  1, 1884, 100  bbl.  rye  meal ;  Jan.  15,  200  bbl. 
rye  meal ;  Feb.  10,  300  bbl.  corn  meal ;  Feb.  20,  10  bbl.  oat 
meal.  Delivered  Jan.  15,  100  bbl.  rye  meal;  Jan  30,  150  bbl. 
rye  meal ;  Feb.  28,  200  bbl.  corn  meal.  What  is  the  amount  of 
storage  due  March  1st,  at  5  cents  a  barrel  per  month  ? 

Note. — When  different  rates  are  charged  for  different  kinds  of  goods 
in  store  at  the  same  time,  a  separate  calculation  must  be  made  for  each 
kind. 

LIFE    INSURANCE. 

566.  Life  Insurance  is  a  contract  by  which  a  company  or 
party  agrees  to  pay  a  certain  sum  of  money  on  the  death  of 
the  person  insured,  or  when  he  reaches  a  certain  age. 

567.  Life  Insurance  Companies  are  divided  into  Stock, 
Mutual,  and  Mixed  (Stock  and  Mutual),  and  Co- Operative 
Companies.    (Arts.  232,  233.) 

Note. — The  first  three  are  defined  under  °  Insurance."    (Art.  229.) 

568.  In  a  Co-Operative  Insurance  Company  each  member  is 
assessed  a  fixed  sum  to  meet  losses  by  deaths  as  they  occur.  This 
sum  is  graduated  according  to  age  at  the  time  of  becoming 
a  member,  and  the  sum  for  which  he  is  insured. 

569.  The  Policy  is  the  Contract  which  specifies  the  rate 
of  premium,  the  parties  to  whom  the  money  is  to  be  paid,  etc. 

Notes. — 1.  The  money  may  be  paid  to  any  one  named  by  the  insured. 
If  payable  to  himself,  it  becomes  a  part  of  his  estate  at  his  death,  and  is 
liable  for  his  debts. 

2.  If  payable  to  another,  it  cannot  be  touched  by  his  creditors  ;  nor  can 
he  in  his  will  deprive  the  party  of  its  benefits. 

3.  The  agreement  is  not  to  indemnify  the  insured  for  a  loss,  as  in  Fire 
and  Marine  Insurance,  but  to  pay  a  specified  sum.  Hence,  a  person  may 
insure  his  life  for  any  amount,  or  in  as  many  Companies  as  he  pleases. 

570.  Policies  vary  according  to  the  nature  of  the  insurance. 
The  more  prominent  are  the  Ordinary,  Limited,  Term,  Endow- 
ment, and  Annuity  Policies. 


Life  Insurance.  237 

Note. — Two  persons  may  insure  by  a  Joint  Policy  and  the  sum 
insured  is  payable  to  the  other  on  the  death  of  either. 

571.  An  Ordinary  Life  Policy  stipulates  to  pay  to  the 
parties  named  in  it,  a  certain  sum  of  money  on  the  death  of 
the  insured,  the  annual  premium  being  paid  during  his  life. 

Note. — The  holder  of  an  Annuity  Policy  receives  a  certain  sum 
every  year  during  his  life.     It  is  secured  by  a  single  cash  payment. 

572.  A  Limited  Policy  is  one  on  which  the  premium  is  paid 
annually  for  a  limited  number  of  years,  specified  at  the  time 
the  policy  is  issued,  or  until  the  death  of  the  insured,  if  that 
should  occur  before  the  end  of  the  period  named. 

Note. — The  premiums  on  this  class  of  policies  are  payable  annually,  or 
all  at  one  time.  If  they  are  all  paid  at  once,  the  insured  receives  an 
annual  dividend  in  cash. 

573.  Term  Policies  are  payable  at  the  death  of  the  insured, 
if  he  dies  during  a  given  term  of  years,  the  annual  premium 
continuing  till  the  policy  expires. 

574.  An  Endowment  Policy  guarantees  the  payment  of  a 
certain  sum  of  money  at  a  specified  period,  and  is  payable  at 
the  death  of  the  insured,  if  he  dies  within  that  period.  It 
becomes  an  endowment  payable  at  the  end  of  the  period  to  the 
insured,  if  he  is  still  living. 

Note. — An  endowment  policy  is  a  combination  of  a  term,  policy  and  a 
pure  endowment.  These  policies  are  issued  for  periods  from  10  to  35 
years,  and  may  be  paid  by  single  payments  or  by  annual  premiums. 

575.  The  Premium  is  a  fixed  sum  paid  annually,  or  at 
stated  periods.  It  varies  according  to  the  expectation  of  life. 
(App.  p.  297.) 

576.  The  Reserve  Fund  is  a  sum  which,  put  at  a  given  rate 
of  interest,  with  the  premiums  on  existing  policies,  is  intended 
to  be  sufficient  to  meet  all  obligations  when  they  become  due. 

Note.— The  legal  rate  of  interest  on  reserve  funds  in  the  State  of  New 
York  is  4|  % ,  in  Massachusetts  4$ , 


238 


Life  Insurance, 


ANNUAI 

PREMIUM   RATES   FOR   AN   INSURANCE    OP    $1000. 

PAYABLE 

AS  INDICATED,   OR  AT  DEATH, 

IF  PRIOR. 

Age. 

At 

In  10 

In  15 

In  20 

In  25 

In  30 

In  35 

Age. 

Death. 

years. 

years. 

years. 

years. 

years. 

years. 

25 

16.91 

100.23 

62.65 

44.46 

34.04 

27.54 

23.30 

25 

26 

17.34 

100.27 

62.71 

44.54 

34.14 

27.66 

23.46 

26 

27 

17.79 

100.32. 

62.77 

44.62 

34.24 

27.80 

23.64 

27 

28 

18.26 

100.38 

62.84 

44.71 

34.36 

27.95 

23.84 

28 

29 

18.76 

100.43 

62.92 

44.80 

34.49 

28.12 

24.06 

29 

30 

19.30 

100.50 

63.00 

44.91 

34.62 

28.30 

24.31 

30 

31 

19.85 

100.56 

63.09 

45.02 

34.78 

28.51 

24.58 

31 

32 

20.44 

100.64 

63.19 

45.15 

34.96 

28.74 

24.89 

32 

33 

21.06 

100.72 

63.29 

45.30 

35.15 

29.00 

25.23 

33 

34 

21.73 

100.81 

63.41 

45.46 

35.36 

29.29 

25.60 

34 

35 

22.42 

100.91 

63.54 

45.64 

35.61 

29.61 

26.01 

35 

36 

23.16 

101.02 

63.69 

45.84 

35.88 

29,97 

26.47 

36 

37 

23.94 

101.14 

63.85 

46.06 

36.18 

30.37 

26.98 

37 

38 

24.78 

101.27 

64.04 

46.31 

36.52 

30.81 

27.54 

38 

39 

25.66 

101.42 

64.24 

46.60 

36.90 

31.30 

28.16 

39 

40 

26.61 

101.58 

64.48 

46.91 

37.32 

31.85 

28.84 

40 

41 

27.60 

101.76 

64.73 

47.27 

37.80 

32.46 

29.59 

41 

42 

28.66 

101.97 

65.03 

47.67 

38.33 

33.14 

30.42 

42 

43 

29.79 

102.21 

65.36 

48.12 

38.92 

33.89 

31.32 

43 

44 

30.99 

102.48 

65.74 

48.63 

39.58 

34.73 

32  31 

44 

45 

32.27 

102.78 

66.17 

49.20 

40.32 

35.65 

83.40 

45 

46 

33.64 

103.13 

66.65 

49.85 

41.15 

36.67 

46 

47 

35.11 

103.53 

67.19 

50.56 

43.07 

37.79 

47 

48 

36.66 

103.98 

67.81 

51.37 

43.09 

39.03 

48 

49 

38.33 

104.49 

68.50 

52.27 

44.23 

40.39 

49 

50 

40.10 

105.06 

69.26 

53.27 

45.48 

41.87 

50 

51 

41.99 

105.70 

70.12 

54.38 

46.86 

51 

52 

44.01 

106.41 

71.08 

55.61 

48.38 

52 

53 

46.16 

107.20 

72.14 

56.98 

50.06 

53 

54 

48.47 

108.08 

73.32 

58.50 

51.89 

54 

55 

50.92 

109.07 

74.63 

60.17 

53.90 

55 

56 

53.55 

110.16 

76.09 

62.02 

56 

57 

56.35 

111.38 

77.71 

64.06 

57 

58 

59.35 

112.73 

79.51 

66.31 

58 

59 

62.56 

114.23 

81.50 

68.78 

59 

60 

65.99 

115.90 

83.71 

71.49 

60 

61 

69.67 

117.75 

86.15 

61 

62 

73.59 

119.81 

88.84 

62 

63 

77.81 

122.09 

91.81 

63 

64 

82.33 

124.63 

95.08 

64 

65 

87.17 

127.43 

98.68 

65 

Life  Insurance. 


239 


577.  The  true  value  of  a  policy  surrendered  is  the  legal 
reserve  less  a  certain  per  cent  for  expenses. 

The  market  value  is  the  sum  the  company  will  pay  the  holder 
on  its  surrender. 

Notes. — 1.  Reserve  Endowment,  Tontine  Investment,  and  some  other 
special  policies,  guarantee  to  pay  the  holder  a  definite  amount  at  the 
termination  of  fixed  periods. 

2.  Some  companies  apply  all  credited  dividends  to  the  continuance  of 
the  insurance.  Others  apply  the  legal  reserve  to  the  purchase  of  term 
insurance  at  the  regular  rates. 

578.  Finding  the  annual  premium  for  an  ordinary  life  or  endow- 
ment policy  when  the  rate  and  sum  insured  are  given  ;  by  the  Tables. 

1.  What  is  the  annual  premium  for  an  ordinary  life  policy  of 
$3000,  issued  to  a  person  35  years  of  age  ? 

Solution. — By  the  Table  the  annual  premium  for  $1000  at  35  years 
of  age  is  $22.42 ;  hence,  for  $3000  it  is  3  times  $22.42  =  $67.26,  Am. 

2.  Find  the  annual  premium  for  an  ordinary  life  policy  of 
$10000,  issued  to  a  person  40  years  old. 

3.  A  young  man  at  the  age  of  25  years  took  out  an  ordinary 
life  policy  of  $20000 ;  he  died  at  the  age  of  45  years ;  how 
much  more  than  he  had  paid  in  premiums  did  his  heirs  receive ; 
no  allowance  heing  made  for  interest  ? 


TABLE   OF   ANNUAL 

KATES 

FOR 

ENDOWMENT 

POLICIES    OF   $1000. 

PAYABLE  AS 

INDICATED. 

Age. 

In  10 

years. 

$103.91 

In  15 
years. 

In  20 

years. 

Age. 

Age. 

In  10 

years. 

In  15 

years. 

In  20 

years. 

Age. 
36 

25 

$66.02 

$47.68 

25 

36 

$105.75 

$68.12 

$50.11 

26 

104.03 

66.15 

47.82 

26 

37 

106.00 

68.41 

50.47 

37 

27 

104.16 

66.29 

47.98 

27 

38 

106.28 

68.73 

50.86 

38 

28 

104.29 

66.44 

4815 

28 

39 

106.58 

69.09 

51.30 

39 

29 

10443 

66.60 

48.33 

29 

40 

106.90 

69.49 

51.78 

40 

30 

104.58 

66.77 

48.53 

30 

41 

107.26 

69.92 

52  31 

41 

31 

104.75 

66  96 

48.74 

31 

42 

107.65 

70.40 

5289 

42 

32 

104.92 

6716 

48.97 

32 

43 

108.08 

70.92 

53.54 

43 

33 

105.11 

67.36 

49.22 

33 

44 

108.55 

7150 

54.25 

44 

34 

105.31 

67.60 

49.49 

34 

45 

109.07 

72.14 

55.04 

45 

35 

105.53 

67  85 

49  79 

35 

46 

109.65 

72.86 

55.91 

46 

240  Life  Insurance. 

4.  A  man  at  the  age  of  32  years  has  an  investment  of  $15000 
at  6%  interest,  which  he  intends  to  leave  his  family  ;  what  will 
be  its  amount  in  25  years  at  compound  interest  ?  How  much 
will  his  family  receive  if  he  takes  out  a  life  policy  and  pays  the 
premium  with  the  interest  on  his  investment  ? 

5.  What  annual  premium  must  I  pay  for  a  twenty-year 
endowment  policy  of  $12000  ;  my  age  being  40  years? 

6.  What  is  the  annual  premium  on  a  20-year  endowment 
policy  for  $16000;  the  age  being  45  years? 

7.  How  much  more  is  received  at  the  expiration  of  the  20 
years,  than  has  been  paid  out  in  annual  premiums  ? 

8.  If  a  person  36  years  of  age  secures  an  endowment  policy 
for  $1000  for  20  years,  payable  to  himself  or  his  heirs,  what 
will  be  his  loss  if  he  survives  and  pays  his  premium  annually? 

9.  A  man  insured  his  life  at  the  age  of  46  years  for  $15000 
on  the  ordinary  life  plan.  He  died  at  the  age  of  75  ;  having 
paid  the  premiums  annually,  how  much  had  the  insurance 
company  received  ?  How  much  would  a  10-year  endowment 
cost  for  the  same  sum  ? 

10.  What  is  the  annual  premium  for  a  15-year  endowment 
policy  of  $12000,  issued  to  a  person  32  years  of  age  ? 

11.  When  46  years  of  age  a  man  took  out  a  10-year  endow- 
ment policy  of  $10000.  He  survived  the  period  of  endow- 
ment ;  having  paid  the  annual  rates,  how  much  less  did  he 
receive  than  he  had  paid  the  company,  reckoning  interest  at 

12.  A  gentleman  at  the  age  of  45  insures  his  life  on  the 
ordinary  life  plan  for  $18000.  How  much  must  be  put  at  5% 
interest  to  meet  the  annual  premiums  ? 

13.  If  he  lived  to  be  65  years  old,  would  his  family  receive 
more,  or  less,  if  the  premiums  were  put  at  h%  interest  in  a 
savings  bank  ?    How  much  ? 

14.  A  lady  35  years  of  age  took  out  a  life  policy  for  $5000 
for  the  benefit  of  her  husband,  paying  the  entire  premium  at 
the  rate  of  $369.91  on  $1000,  in  one  payment.  She  died  in  5 
years  after  securing  the  policy  ;  how  much  less  would  the 
company  have  received  if  she  had  paid  the  premium  at  the 
annual  rates  ? 


Annuities,  241 


ANNUITIES. 

579.  An  Annuity  is  a  specified  sum  of  money  paid  annually, 
or  at  equal  periods  ;  as,  semi-annually,  quarterly,  monthly;  to 
continue  a  given  number  of  years,  for  life,  or  forever. 

580.  A  Perpetual  Annuity  is  one  of  unlimited  duration. 

581.  A  Certain  Annuity  begins  and  ends  at  a  fixed  time. 

582.  A  Contingent  Annuity  depends  upon  some  unforeseen 
event,  as  the  death  of  an  individual,  or  his  arrival  at  a  certain 
age.  Life  Insurance,  Pensions,  Dowers,  Leases,  etc.,  belong 
to  this  class  of  incomes. 

583.  An  Annuity  in  Possession  or  an  Immediate  Annuity  is 
one  that  begins  immediately.  When  the  Annuity  begins  at 
some  future  time  it  is  called  a  Deferred  Annuity,  or  Annuity 
in  Reversion. 

Note. — The  term  of  reversion  may  be  definite  or  contingent. 

584.  If  Annuities  are  not  paid  when  due,  they  are  said  to 
he  forborne,  or  in  arrears, 

585.  The  Present  Value  of  an  Annuity  is  the  sum  which,  at 
the  given  rate  of  interest,  will  amount  to'  its  final  value. 

586.  The  Amount  or  Final  Value  of  an  Annuity  is  the  sum 
which  all  its  payments  with  interest  on  each  will  amount  to 
at  its  termination. 

Note. — Annuities,  like  debts,  are  entitled  to  interest  after  they  are  due. 

587.  Annuities  at  Simple  Interest  are  computed  by  the 
principles  of  Arithmetical  Progression,  the  Annuity  being  the 
first  term  ;  the  interest  of  the  annuity  for  1  year,  the  common 
difference ;  the  time  in  years,  the  number  of  terms ;  and  the 
annuity  plus  the  interest  due  on  it  for  the  number  of  years  less 
1,  the  last  term. 

16 


242  At  8i7nple  Interest 

588.  To  find  the  Amount  or  Final  Value  of  an  Annuity  at 
Simple  Interest,  when  the  Time  and  Rate  are  given. 

1.  What  is  the  amount  of  $100  annuity  for  5  years,  at  6%  ? 

Analysis. — The  first  annuity  is  not  due  until  the  end  of  the  first  year, 
and  draws  interest  only  from  the  time  it  falls  due.  The  second  is  not  due 
until  the  end  of  the  second  year,  and  draws  interest  1  year  less  than  the 
first ;  the  third  one  year  less  than  the  second;  and  so  on  till  all  the  pay- 
ments are  made.     Hence,  the  arithmetical  series 

100  +  (6x4),  +  100  +  (6x3),  +  100  +  (6x2),  +100  +  6,  +100. 

589.  The  last  payment  equals  the  given  annuity  plus  the 
product  of  the  annual  interest  by  the  number  of  payments 
less  1. 

590.  The  terms  are  now  the  annuity  or  first  payment,  the  last 
payment,  and  the  number  of  payments,  to  find  the  sum  of  all 
the  payments. 

The  sum  of  the  two  extremes,  100  +  124  =  224,  and  224-T-2  =  112,  the 
average  value  of  all  the  payments.  Now,  112  x  5  =  560,  the  sum  or  final 
value  of  the  annuity.    Hence,  the 

Eule. — I.  To  the  annuity  add  the  product  of  the 
annual  interest  of  the  annuity  by  the  number  of  pay- 
ments less  1,  for  the  last  payment. 

II.  Multiply  half  the  sum  of  the  first  and  last  pay- 
ments by  the  number  of  payments,  and  the  product  will 
be  the  final  value  of  the  annuity. 

2.  What  is  the  amount  of  an  annuity  of  $150  for  8  years, 
when  money  is  worth  6%  simple  interest  ? 

591.  To  find  the  Present  Worth  of  Annuities  at  Simple  Interest. 

3.  What  is  the  present  worth  of  $1 20  annuity  for  4  yr.,  at  7%? 

Solution. — By  the  preceding  rule  the  final  value  of  the  annuity  is 
$530.40.  The  present  worth  of  $530.40  due  in  4  years,  at  7%  simple 
interest  —  $414,375  (Art.  310).     Hence,  the 

Rule. — First  find  the  amount  or  final  value  of  the 
given  annuity  for  the  given  time  and  rate ;  then  find 
the  present  worth  of  this  amount  as  in   true  discount. 

4.  What  is  the  present  worth  of  $600  annuity  for  8  yr.,  at  6%? 


Annuities.  243 


ANNUITIES    AT    COMPOUND    INTEREST. 

592.  Annuities  at  compound  interest  are  computed  by  the 
principles  of  Geometrical  Progression,  the  annuity  being  the 
first  term;  the  amount  of  $1  for  1  year,  the  ratio;  the 
number  of  payments,  the  number  of  terms,  and  the  annuity 
multiplied  by  the  amount  of  $1  for  1  year  or  period,  raised  to 
the  power  whose  index  is  1  less  than  the  number  of  payments, 
is  the  last  term. 

l.  What  is  the  amount  or  final  value  of  an  annuity  of  $100 
for  4  years,  at  Q%  compound  interest. 

Analysis. — The  first  annuity  is  not  due  until  the  end  of  the  first  year 
or  period ;  the  second  is  not  due  until  the  end  of  the  second  year  or  period, 
and  draws  interest  1  year  less  than  the  first ;  the  third  draws  interest  1 
year  less  than  the  second,  and  so  on  until  all  the  payments  are  made. 
Hence,  assuming  $1  for  the  annuity,  we  have  the  following  series : 

$1,  1  x  1.06,  1  x  (1.06  x  1.06),  1  x  (1.06  x  1.06  x  1.06) ; 

or,  $1,  1  x  1.06,  1  x  (1.06)2,  1  x  (1.06)3,  etc. 

That  is,  each  successive  term  =  the  1st  term  xby  the  ratio  raised  to  a 
power  whose  index  is  1  less  than  the  number  of  the  term.  Therefore,  the 
last  term  =  100  x  1.191016  =  119.1016.    Hence, 

593.  To  find  the  last  term  or  payment 

Multiply  the  first  term  by  that  -power  of  the  ratio 
denoted  by  1  less  than  the  number  of  terms. 

594.  The  terms  are  now  the  annuity  or  first  payment,  the  last 
payment,  and  the  ratio,  to  find  the  sum  of  all  the  payments. 

Since,  $100  (annuity)  x  (1.06)3  =  $119.1016,  the  last  payment, 
$119.1016x1.06,  the  ratio,  =  $126.247696.  Then,  $126.247696  -  $100 
(annuity)  =  $26.247696  ;  and  $26.247696  -h  .06  =  $437.4616,  the  sum  of 
the  terms,  or  final  value  of  annuity.     Hence,  the 

Rule. — Multiply  the  last  term  by  the  ratio,  and  sub- 
tracting the  first  term  from  the  product,  divide  the 
remainder  by  the  ratio  less  1. 

Note.— The  labor  of  computing  annuities  at  Compound  Interest  is 
greatly  diminished  by  the  use  of  the  following  tables : 


244 


At  Compound  Interest. 


Table    I. 

595.  Amount  of  $1  annuity  at  Compound  Interest,  from 
1  year  to  40,  inclusive. 


Yrs. 

1 

8*. 

8tf. 

4* 

ft. 

w. 

7%. 

Yrs. 

1.000  000 

1.000  000 

1  000  000 

1.000  000 

1.000  000 

1.000  000 

1 

2 

2.030  000  1    2.035  000 

2.040  000 

2.050  000 

2.060  000 

2.070  000 

2 

3 

3.090  900      3.106  225 

3.121  600 

3.152  500 

3.183  600 

3.214  900 

3 

4: 

4.183  627 

4.214  943 

j    4.246  464 

4.310  125 

4.374  616 

4.439  943 

4 

5 

5.309  136 

5.362  466 

5.416  323 

5.525  631 

5.637  093 

5.750  739 

5 

6 

6.468  410 

6.550  152 

6.632  975 

6.801  913 

6.975  319 

7.153  291 

6 

7 

7.662  462 

7.779  408 

7.898  294 

8.142  008 

8.393  838 

8.654  021 

7 

S 

8.892  336 

9.051  687 

9.214  226 

9.549  109 

9.897  468 

10.259  803 

8 

9 

10.159  106    10.368  496 

10.582  795 

11.026  564 

11.491  316 

11.977  989 

9 

10 

11.463  879 

11.731  393 

12.006  107 

12.577  893 

13.180  795 

13.816  448 

10 

11 

12.807  796    13.141  992 

13.486  351 

14.206  787 

14.971  643 

15.783  599 

11 

12 

14.192  030    14.601  962 

15.025  805 

15.917  127 

16.869  941 

17.888  451 

12 

13 

15.617  790 

16.113  030 

16.626  838 

17.712  983 

18.882  138 

20.140  643 

13 

14 

17.086  324 

17.676  986 

18.291  911 

19.598  632 

21.015  066 

22.550  488 

14 

15 

18.598  914 

19.295  681 

20.023  588 

21.578  564 

23.275  970 

25.129  022 

15 

16 

20.156  881 

20.971  030 

21.824  531 

23.657  492 

25.670  528 

27.888  054 

16 

17 

21.761  588 

22.705  016 

23.697  512 

25.840  366 

28.212  880 

30.840  217 

17 

18 

23.414  4,35 

24.499  691 

25.645  413 

28.132  385 

30.905  653 

33.999  033 

18 

19 

25.116  868 

26.357  180 

27.671  229 

30.539  004 

33.759  992 

37.378  965 

19 

20 

26.870  374 

28.279  682 

29.778  079 

33.065  954 

36.785  591 

40.995  492 

20 

21 

28.676  486 

30.269  471 

31.969  202 

35.719  252 

39.992  727 

44.865  177 

21 

22 

30.536  780 

32.328  902 

34.247  970 

38.505  214 

43.392  290 

49.005  739 

22 

23 

32.452  884 

34.460  414 

36.617  889 

41.430  475 

46.995  828 

53.436  141 

23 

24 

34.426  470 

36.666  528 

39.082  604 

44.501  999 

50.815  577 

58.176  671 

24 

25 

36.459  264 

38.949  857 

41.645  908 

47.727  099 

54.864  512 

63.249  030 

25 

26 

38.553  042 

41.313  102 

44.311  745 

51.113  454 

59.156  383 

68.676  470 

26 

27 

40.709  634 

42.759  060 

47.084  214 

54.669  126 

63.705  766 

74.483  823 

27 

28 

42.930  923 

46.290  627 

49.967  583 

58.402  583 

68.528  112 

80.697  691 

28 

29 

45.218  850 

48.910  799 

52.966  286 

62.322  712 

73.639  798 

87.346  529 

29 

30 

47.575  416 

51.622  677 

56.084  938 

66.438  848 

79.058  186 

94.460  786 

30 

31 

50.002  678 

54.429  471 

59.328  335 

70.760  790 

84.801  677 

102.073  041 

31 

32 

52.502  759 

57.334  502 

62.701  469 

75.298  829 

90.899  778 

110.218  154 

32 

33 

55.077  841 

60.341  210 

66.209  527 

80.063  771 

97.343  165 

118.933  425 

33 

34 

57.730  177 

63.453  152 

69.857  909 

85.066  959 

104. 183  755 

128.258  765 

34 

35 

60.462  082 

66.674  013 

73.652  225 

90.320  307 

111.434  780 

138.236  878 

35 

36 

63.271  944 

70.C07  603 

77.598  314 

95.836  323 

119.120  867 

148.913  460 

36 

37 

66.174  223 

73.457  869 

81.702  246 

101.628  139 

127.268  119 

160.337  400 

37 

38 

69.159  449 

77.028  895 

85.970  336 

107.709  546  | 

135.904  206 

172.561  020 

38 

39 

72.234  238    80.721  906 

90.409  150 

114.0D5  028 

145.058  458 

185.640  292 

39 

40 

75.401  260  !  84.550  278 

1 

95.025  516 

120.7!)!)  774 

154.761  C66 

199.635  112 

40 

Annuities. 


245 


Tab  le    II. 

596.  Present  Worth  of  $1  annuity  at  Compound  Interest, 
from  1  year  to  40,  inclusive. 


Yrs. 

1 

3*. 

SK*. 

<¥. 

5*. 

6£. 

7%. 

Yrs. 

0.970  874 

0.966  184 

0.961  538 

0.952  381 

0.943  396 

0.934  579 

1 

2 

1.913  470 

1.899  694 

1.886  095 

1.859  410 

1.833  393 

1.808  017 

2 

3 

2.828  611 

2.801  637 

2.775  091 

2.723  248 

2.673  012 

2.624  314 

3 

4 

3.717  098 

3.673  079 

3.629  895 

3.545  951 

3.465  106 

3.387  209 

4 

5 

4.579  707 

4.515  052 

4.451  822 

4.329  477 

4.212  364 

4.100  195 

5 

6 

5.417  191 

5.328  553 

5.242  137 

5.075  692 

4.917  324 

4.766  537 

6 

7 

6.230  283 

6.114  544 

6.002  055 

5.786  373 

5.582  381 

5.389  286 

7 

8 

7.019  692 

6.873  956 

6.732  745 

6.463  213 

6.209  744 

5.971  295 

8 

9 

7.786  109 

7.607  687 

7.435  332 

7.107  822 

6.801  692 

6.515  228 

9 

10 

8.530  203 

8.316  605 

8.110  896 

7.721  735 

7.360  087 

7.023  577 

10 

11 

9.252  624 

9.001  551 

8.760  477 

8.306  414 

7.886  875 

7.498  669 

11 

12 

9.954  004 

9.663  334 

9.385  074 

8.863  252 

8.383  844 

7.942  671 

12 

13 

10.034  955 

10.302  738 

9.985  618 

9.393  573 

8.852  683 

8.357  635 

13 

14 

11.296  073 

10.920  520 

10.568  123 

9.898  641 

9.294  984 

8.745  452 

14 

15 

11.937  935 

11.517  411 

11.118  387 

10.379  658 

9.712  249 

9.107  898 

15 

16 

12.561  102 

12.094  117 

11.652  296 

10.837  770 

10.105  895 

9.446  632 

16 

17 

13.166  118 

12.651  321 

12.165  669 

11.274  066 

10.477  SCO 

9.763  206 

17 

18 

13.753  513 

13.189  682 

12.659  297 

11.689  587 

10  827  603 

10.059  070 

18 

19 

14.323  799 

13.709  837 

13.133  939 

12.085  321 

11.158  116 

10.335  578 

19 

20 

14.877  475 

14.212  403 

13.590  326 

12.462  210 

11.469  421 

10.593  997 

20 

21 

15.415  024 

14.697  974 

14.029  160 

12.821  153 

11.764  077 

10.835  527 

21 

22 

15.936  917 

15.167  125 

14.451  115 

13.163  003 

12.041  582 

11.061  241 

22 

23 

16.443  608 

15.620  410 

14.&56  842 

13.488  574 

12.303  379 

11.272  187 

23 

24 

16.935  542 

16.058  368 

15.246  963 

13.798  642 

12.550  358 

11.469  334 

24 

25 

17.413  148 

16.481  515 

15.622  080 

14.093  945 

12.783  356 

11.653  583 

25 

26 

17.876  842 

16.890  352 

15.982  769 

14.275  185 

13.003  166 

11.825  779 

26 

27 

18  327  031 

17.285  365 

16.329  586 

14.643  034 

13.210  534 

11.986  709 

27 

28 

18.764  108 

17.667  019 

16.663  063 

14.898  127 

13.406  164 

12.137  111 

28 

29 

19.188  455 

18.035  767 

16.983  715 

15.141  074 

13.590  721 

12.277  674 

29 

30 

19.600  441 

18.392  045 

17.292  033 

15.372  451 

13.764  831 

12.409  041 

30 

31 

20.000  428 

18.736  276 

17.588  494 

15.592  811 

13.929  086 

12.531  814 

31 

32 

20.. 338  766 

19.068  865 

17.873  552 

15.802  677 

14.084  043 

12.646  555 

32 

33 

20.765  792 

19.390  208 

18.147  646 

16.002  549 

14.230  230 

12.753  790 

33 

34 

21.131  837 

19.700  684 

18.411  198 

16.192  204 

14.368  141 

12.854  009 

34 

35 

21 .487  220 

20.000  661 

18.664  613 

16.374  194 

14.498  246 

12.947  672 

35 

36 

21.a32  252 

20.290  494 

18.908  282 

16.546  852 

14.620  987 

13.035  208 

36 

37 

22.167  235 

20.570  525 

19.142  579 

16.711  287 

14.736  780 

13.117  017 

37 

38 

22.492  462 

20.841  087 

19.367  864 

16.867  893 

14.846  019 

13.193  473 

38 

39 

22.808  215 

21.102  500 

19.584  485 

17.017  041 

14.949  075 

13.264  928 

39 

40 

23.114  772 

21.355  072 

19.792  774 

17.159  086 

15.046  297 

13.331  709 

40 

246  Annuities. 

597.  To  find  the  amount  or  Final  Value  of  an  Annuity. 

Kule. — Multiply  the  tabular  amount  of  $1  by  the 
annuity,  the  product  will  be  the  final  value.     (Table  I.) 

Note.  —When  payments  are  made  semi-annually,  take  from  the  table 
twice  the  given  number  of  years,  and  £  the  given  rate  of  interest. 

2.  What  is  the  final  value  of  $600  for  8  years,  at  6%  ? 

Solution.— Tab.  Amt.  of  $1,  at  6%  for  8  years  =  $9.897468  ;  and 
$9.897468  x  600  =  $5938.4808,  Ans. 

3.  What  is  the  final  value  of  an  annual  pension  of  $150  for 
15  years,  at  4$  ? 

4.  A  widow  is  entitled  to  $140  a  year  for  18  years,  at  10% 
semi-annual  compound  interest ;  what  is  its  final  value  ? 

598.  To  find  the  Present  Value  of  an  Annuity. 

Kule. — Multiply  the  present  worth  of  $1  by  the  Given 
Annuity.     (Table  II.) 

5.  What  is  the  present  worth  of  $300  due  in  7  years,  at  6%  ? 

Solution.— Present  worth  of  $1,  at  6%  for  7  yr.  =  $5.582381 ;  and 
$5.582381  x  300  =  $1674.7143,  Ans. 

6.  What  is  the  present  worth  of  an  annual  ground  rent  of 
$500,  at  4%,  for  12  years  ? 

7.  What  is  the  present  worth  of  an  annuity  of  $500  for  8 
years,  at  4%  ? 

8.  What  is  the  present  worth  of  an  annuity  of  $3000,  at  %%, 
for  20  years  ? 

599.  To  find  the  Present  Worth  of  an  Annuity  in  Reversion. 

Kule. — Find  the  present  worth  of  $1  to  the  time  the 
annuity  begins,  also  to  the  time  it  ends ;  and  multiply 
the  difference  between  these  values  by  the  given  annuity. 


Annuities.  247 

9.  What  is  the  present  worth  of  an  annuity  in  reversion  of 
$1000,  at  6%,  which  begins  in  3  years,  and  then  terminates 
after  5  years  ? 

Solution.— The  present  worth  of  $1,  at  6%  for  3  yr.  =  $2.673012 

"8  yr.  =  $6.209744 
Their  difference  $3.536732  x  1000  (annuity)  =  $3536.732,  Ans. 

10.  The  reversion  of  a  lease  of  $450  per  year,  at  h%,  begins  in 
3  years  and  continues  9  years;  what  is  its  present  worth  ? 

li.  A  father  bequeathed  his  son,  11  yrs.  of  age,  a  5%  annuity 
of  $1000,  to  begin  in  3  years  and  continue  10  years  ;  what 
would  be  the  amount  when  the  son  was  21  years  old  ?  What 
is  its  present  worth  ? 

600.   To  find  the  Present  Worth  of  a  Perpetual  Annuity. 

Eule. — Divide  the  given  annuity  by  the  interest  of  $1 
for  1  year,  at  the  given  per  cent. 

12.  A  man  wished  to  establish  a  perpetual  professorship  in  a 
college,  at  $2000  a  year ;  what  sum  must  he  invest  in  Gov't  5's 
to  yield  this  income  ? 

Solution.— $2000. 00 -^-.  05  =  $40000,  Ans. 

13.  An  estate  in  New  York  pays  $3000  annually,  at  6% 
interest,  on  a  perpetual  ground  rent ;  what  is  the  value  of  the 
estate  ? 

Note. — When  the  annuity  is  payable  for  any  period  less  than  a  year, 
before  dividing  by  the  interest  of  $1  for  1  year,  the  annuity  must  be 
increased  by  the  interest  which  may  accrue  on  the  parts  of  the  annuity 
payable  before  the  end  of  the  year. 

14.  What  is  the  present  worth  of  a  perpetual  annuity  of 
$250  in  arrears  for  10  years,  allowing  ?>%  compound  interest. 

Note. — There  is  now  due  the  amount  of  $250  annuity  for  10  yr.  at  3%, 
which  must  be  added  to  the  present  worth  of  the  perpetuity. 

15.  What  is  the  present  worth  of  a  perpetuity  of  $500,  in 
arrears  for  30  years,  allowing  compound  interest  at  5  per 
cent? 


248  Sinking  Funds. 


SINKING    FUNDS. 

601.  Sinking  Funds  are  sums  of  money  set  apart  at  regular 
periods  for  the  payment  of  indebtedness.  They  are  properly 
derived  from  an  excess  of  income  above  expenses.* 

602.  To  find  what  sum  must  be  set  apart  annually,  as  a  sinking 
fund,  to  pay  a  given  debt  in  a  given  time. 

1.  A  certain  town  borrowed  $20000  to  build  a  Union  School- 
house,  and  agreed  to  pay  6%  compound  interest;  what  sum 
must  be  set  apart,  as  a  sinking  fund  annually,  to  pay  the  debt 
in  10  years  ? 

Analysis.— The  amt.  of  $1  at  6%  comp.  int.  for  10  yrs.  is  $1.790848, 
and  that  of  $20000  is  20000  times  as  much,  or  $35816.96.    (Art.  306.) 

Again,  the  amt.  of  an  annual  payment  or  annuity  of  $1  at  6%  for  10 
yrs.  is  $13.180795  ;  since  to  pay  $13.180795  requires  an  annuity  of  $1  at 
6%  for  10  yrs.,  a  debt  of  $35816.96  will  require  35816.96-T-13. 180795  = 
$2717.36,     Ans.     Hence,  the 

Rule. — Divide  the  amount  of  the  debt  at  its  maturity, 
at  compound  interest,  by  the  amount  of  an  annuity  of  $1 
for  the  given  time  and  rate,  and  the  quotient  will  be  the 
sinking  fund  required. 

2.  What  sum  must  be  set  apart  annually  to  rebuild  a  bridge 
costing  $30000,  estimated  to  last  17  years,  allowing  5%  com- 
pound interest  ? 

3.  A  railroad  company  bought  $100000  worth  of  rolling 
stock,  payable  in  5  yr.  with  %%  compound  int. ;  what  sum  must 
be  set  apart  annually  as  a  sinking  fund  to  discharge  the  debt  ? 

4.  The  National  debt  of  the  United  States  is  about 
$2,003,000,000  ;  what  must  be  the  excess  annually  of  revenue 
over  expenditure,  allowing  5%  comp.  interest  to  pay  the  debt 
in  21  years. 

*  Sinking  Funds  were  first  introduced  into  England  in  1716,  and  renewed  in  H86  by- 
Messrs.  Price  and  Pitt,  who  contended  that  by  applying  a  certain  amount  of  revenue  to 
the  purchase  of  stocks  the  dividends  of  which  should  be  reinvested  in  the  same  manner 
a  sinking  fund  would  be  established,  which  at  compound  interest  would  increase  so  that 
the  largest  debt  might  be  paid.  But  the  fallacy  of  this  idea  was  proven  by  Dr.  Hamilton, 
who  showed  that  the  sinking  fund  had  really  added  to  the  debt,  and  demonstrated  that 
the  only  true  sinking  fund  consists  in  an  excess  of  revenue  above  expenditure. 


Sinking  Funds.  249 

603.  To  find  the  number  of  years  required  to  pay  a  given  debt, 
by  a  given  annua!  sinking  fund. 

5.  A  village  built  a  school-house  costing  $12000,  and  raised 
$1700  a  year  to  pay  for  it ;  allowing  6%  compound  interest, 
how  many  years  will  it  require  to  cancel  the  debt? 

Analysis.— Since  a  sinking  fund  of  $1700  at  6%  for  a  certain  time  has 
a  present  worth  of  $12000,  a  sinking  fund  of  $1,  for  the  same  time  and 
rate,  has  a  present  worth  of  TTVir  Pa*t  as  much  ;  and  $12000 ---$1700  = 
$7.05882.  Looking  in  Table  (Art.  596)  in  col.  6%,  the  time  correspond- 
ing with  this  present  worth  of  $1  is  9  years,  which  is  the  number  of  whole 
years  required,  with  a  balance  due  of  $738 .51. 

The  amt.  of  the  debt  $12000  at  6%  comp.  int.  in  9  yr.  =  $20273.748 
The  amt.  of  s.  fund  $1700         "  "        "        "        =    19535.238 

Balance  due  at  the  end  of  9  yr $738.51 

Hence,  the 

Eule. — Divide  the  debt  by  the  given  sinking  fund,  and 
the  quotient  will  be  the  present  worth  of  $1  for  the  time. 
Loolc  for  this  number  in  Table  (Art.  596)  in  the  col. 
denoting  the  given  rate,  and  opposite  in  the  column  of 
time  will  be  found  the  number  of  years. 

Notes. — 1.  If  the  exact  number  is  not  found  in  the  column  take  the 
years  standing  opposite  the  next  smaller  number. 

2.  To  ascertain  the  balance  due*  at  the  end  of  the  number  of  whole 
years,  find  the  difference  between  the  amount  of  the  debt  at  the  given  rate 
for  the  time  taken  out,  and  the  amount  of  the  sinking  fund  for  the  same 
time  and  rate.     (Tables,  Arts.  595,  «306.) 

6.  The  national  debt  of  Great  Britain  is  about  £800,000,000; 
allowing  5%  compound  interest,  how  many  years  would  it 
require  to  cancel  it  by  an  annual  sinking  fund  of  £48,000,000  ? 

7.  The  national  debt  of  France  is  about  $4,750,000,000  ; 
allowing  3%  int.,  how  long  would  it  take  to  discharge  it  by  a 
sinking  fund  of  $200,000,000  a  year  ? 

8.  The  Dom.  of  Canada  had  a  debt  in  1881  of  $199861537, 
and  a  sinking  fund  of  $44465757;  allowing  4$  int.,  how 
many  years  will  be  required  to  cancel  the  debt? 


250  Sinking  Funds. 

604.  To  find  the  amount  of  a  sinking  fund,  the  rate  of  interest 
and  the  time  being  given. 

9.  If  a  Railroad  Co.  sets  apart  an  annual  sinking  fund  of 
$20000,  and  puts  it  at  7%  compound  interest,  what  will  be  its 
amount  in  10  years  ? 

Analysis. — The  amount  of  a  sinking  fund  of  $1  in  10  jr.,  at  7%,  is 
$13.816448  (Table,  Art.  595) ;  therefore,  the  amount  for  the  same  time 
and  rate  of  a  sinking  fund  of  $20000  =  13.816448x20000  =  $276328.96. 
Hence,  the 

Eule. — Multiply  the  amount  of  $1  for  the  given  time 
and  rate  as  found  in  Art.  595  by  the  annual  sinking 
fund. 

10.  What  will  be  the  amount  in  12  years  of  a  sinking  fund 
of  $12000,  yielding  5%  compound  interest  ? 

605.  Sinking  Fund  Bonds  are  securities  issued  by  Corpora- 
tions, based  on  the  pledge  of  a  special  income  which  is  fancied 
for  their  redemption. 

Note. — This  income  is  derived  in  the  case  of  Railroads  from  the  sale 
of  lands,  from  rents,  etc.,  or  from  a  per  cent  of  the  earnings.  These 
bonds  are  bought  and  sold  in  the  stock  market  like  Mortgage  Bonds. 

11.  A  Kailroad  Co.  issued  sinking  fund  bonds  at  6%  for 
$200000,  payable  in  10  years;  if  at  compound  interest,  what 
sum  must  be  set  apart  annually  to  meet  interest  and  principal 
when  due  ?     (Art.  602.) 

12.  What  would  be  the  amount  in  10  years,  at  6%  simple 
interest  ? 

13.  If  the  funded  securities  were  drawing  an  annual  income 
of  4:%  compound  interest,  by  how  much  would  the  amount 
necessary  to  meet  principal  and  interest  at  6%  be  reduced  ? 

14.  With  the  above  reduction  what  sum  would  be  needed 
annually  as  a  sinking  fund  to  pay  the  amount  when  due  at  4$  ? 


f 


OWER8    and 


606.  A  Power  is  a  product  of  equal  factors. 
Thus,  2x2x2  =  8,  and  3x3  =  9;  8  and  9  are  powers. 

Note. — Powers  are  named  according  to  the  number  of  times  the  equal 
factor  is  taken  to  produce  the  given  power. 

607.  The  First  Power  is  the  number  itself. 

608.  The  Second  Power  is  the  product  of  a  number  taken 
twice  as  a  factor,  and  is  called  a  Square. 

609.  The  Third  Power  is  the  product  of  a  number  taken 
three  times  as  a  factor,  and  is  called  a  Cube. 

610.  An  Exponent  is  a  small  figure  placed  above  a  number 
on  the  right  to  denote  the  power. 

It  shows  that  the  number  above  which  it  is  placed  is  to  be 
raised  to  the  power  indicated  by  this  figure.     Thus, 

611.  The  expression  24  is  read,  "2  raised   to  the  fourth 
power,  or  the  fourth  power  of  2." 

1.  Express  the  4th  power  of  84.       3.  The  7th  power  of  350. 

2.  Express  the  5th  power  of  248.     4.  The  8th  power  of  461. 

612.  To  find  any  required  Power  of  a  Number. 

5.  What  is  the  5th  power  of  8  ? 
Solution.— 85  -8x8x8x8x8  =  32768,  Ans. 

Rule. — Take  the  number  as  many  times  as  a  factor  as 
there  are  units  in  the  exponent  of  tli  e  required  power. 


252  Powers  and  Roots. 

Notes. — 1.  A  common  fraction  is  raised  to  a  power  by  involving  each 
term.     Thus,  (f)8  =  TV 

2.  A  mixed  number  should  be  reduced  to  an  improper  fraction,  or  the 
fractional  part  to  a  decimal ;  then  proceed  as  above. 

Thus,  (2£)2  =  (|)2  =  -2¥5- ;  or  2£  =  2.5  and  (2.5)2  =  6.25. 

3.  All  powers  of  1  are  1 ;  for  1  x  1  x  1,  etc.  =  1. 

613.  A  Root  is  one  of  the  equal  factors  of  a  number. 
Note. — Boots  are  named  from  the  number  of  equal  factors  they  contain. 

614.  The  Square  Root  is  one  of  the  two  equal  factors  of  a 
number. 

Thus,  5  x  5  =  25  ;  therefore,  5  is  the  square  root  of  25. 

615.  The  Cube  Root  is  one  of  the  three  equal  factors  of  a 
number. 

Thus,  3  x  3  x  3  —  27 ;  therefore,  3  is  the  cube  root  of  27,  etc. 

616.  The  character  (y')  is  called  the  Radical  Sign. 

Note. — It  is  a  corruption  of  the  letter  R,  the  initial  of  the  Latin  radix, 
a  root. 

617.  Roots  are  denoted  in  two  ways : 

1st.  By  prefixing  to  the  number  the  Radical  Sign,  with  a 
figure  placed  over  it  called  the  Index  of  the  root ;  as  ^/4,  ^/8. 

2d.  By  a  fractional  exponent  placed  above  the  number  on 
the  right.  Thus,  9*,  27*,  denote  the  square  root  of  9,  and  the 
cube  root  of  27. 

Notes. — 1.  The  figure  over  the  radical  sign  and  the  denominator  of 
the  exponent,  each  denote  the  name  of  the  root. 

2.  In  expressing  the  square  root,  it  is  customary  to  use  simply  the 
radical  sign  (\/)>  the 2  being  understood.  Thus,  the  expression  <y/25  =  5, 
is  read,  "  the  square  root  of  25  =  5." 

618.  A  Perfect  Power  is  a  number  whose  exact  root  can  be 
found;  as,  9,  16,  25,  etc. 


Square  Boot.  253 

619.  An  Imperfect  Power  is  a  number  whose  exact  root  can 
not  be  found.     This  root  is  called  a  Surd. 

Thus,  5  is  an  imperfect  power,  and  its  square  root  2.23+  is  a  surd. 

Note. — All  roots  as  well  as  powers  of  1,  are  1. 

SQUARE    ROOT. 

620.  Extracting  the  Square  Root  is  finding  one  of  two  equal 
factors  of  a  number.  (For  demonstration,  see  Complete  Grad. 
Arith.,  Art.  733.) 

621.  To  extract  the  square  root  of  a  number. 
l.  Find  the  square  root  of  5625. 


49 


725 

725 


Explanation. — Since  the  number  consists  of  two  operation. 

periods  of  two  figures  each,  its  root  will  have  two  of  25  ( 78 

figures.    The  greatest  square  in  the  first  period  is  49, 
its  root  is  7,  which  is  placed  in  tlie  quotient.     Sub- 
tracting this  square  from  the  left  hand  period  and       145 
placing  the  next  period  on  its  right,  the  dividend  is 
725.     Doubling  the  root  found  for  a  trial  divisor,  and 
taking  the  first  two  figures  for  a  trial  dividend,  the 
next  quotient  figure  is  5  ;  writing  this  also  in  the  divisor,  multiplying  the 
divisor  thus  completed  by  this  last  figure  of  the  root,  and  subtracting 
there  is  no  remainder.     Therefore,  75  is  the  required  root.    Hence,  the    . 


General     Rule. 

I.  Separate-  the  number  into  periods  of  two  figures 
each,  beginning  at  units,  and  count  both  ways. 

II.  Find  the  greatest  square  in  the  first  period  on  the 
left,  and  place  its  root  on  the  right.  Subtract  this 
square  from  the  period,  and  on  the  right  of  the  remain- 
der place  the  next  period  for  a  dividend. 

III.  Double  the  part  of  the  root  thus  found  for  a  trial 
divisor ;  and  finding  how  many  times  it  is  contained  in 
the  dividend,  omitting  the  right  hand  figure,  annex  the 
quotient  both  to  the  root  and  to  the  divisor. 


254  Powers  and  Hoots. 

IV.  Multiply  the  divisor  thus  increased  by  the  last 
figure  placed  in  the  root,  subtract  the  product  from  the 
dividend,  and  place  the  next  period  on  the  right  of  the 
remainder. 

V.  Proceed  as  before,  till  the  root  of  all  the  periods 
is  found. 

Notes. — 1.  If  there  is  a  remainder  after  the  root  of  the  last  period  is 
found,  annex  periods  of  ciphers,  and  proceed  as  before.  The  figures  of  the 
root  thus  obtained  will  be  decimals. 

2.  If  the  trial  divisor  is  not  contained  in  the  dividend,  annex  a  cipher 
both  to  the  root  and  to  the  divisor,  and  bring  down  the  next  period. 

3.  It  sometimes  happens  that  the  remainder  is  larger  than  the  divisor; 
but  it  does  not  necessarily  follow  that  the  figure  in  the  root  is  too  small. 

4.  The  left  hand  period  in  whole  numbers  may  have  but  one  figure  ; 
but  in  decimals,  each  period  must  have  two  figures.  Hence,  if  the  number 
of  decimals  is  odd,  a  cipher  must  be  annexed  to  complete  the  period. 

Find  the  square  root  of  the  following  numbers : 

2.  2916.  5.  .0784.  8.  .00953361. 

3.  531441.  6.  .766961.  9.  617230.2096. 

4.  287.65.  7.  1073.741.  10.  3685.000289. 

622.  To  find  the  Square  Root  of  Fractions. 

11.  What  is  the  square  root  of  -^? 

Solution.— ^/^  =  f,  Am.    Hence,  the 

KulE. — Reduce  the  fraction  to  its  simplest  form  and 
find  the  square  root  of  each  term  separately. 

Notes.— 1.  If  either  term  of  the  given  fraction,  when  reduced,  is  an 
imperfect  square,  reduce  the  fraction  to  a  decimal,  and  proceed  as  above. 

2.  Mixed  numbers  should  be  reduced  to  improper  fractions,  or  the 
fractional  part  to  a  decimal. 

12.  What  is  the  square  root  of  ^  ?  A?is.  .375,  or  f. 


i3.  ViR  =  ? 


Square  Root 

15.  vm  =  ? 


255 


14.  VA¥W  =  ?  is.  V 

17.  What  is  the  square  root  of  28$  ? 
Solution. -28|  =  H1  and  V1!1  =  V  = 


623.  27*e  square  described  on  the 
hypothenuse  of  a  right-angled  triangle  is 
equal  to  the  sum  of  the  squares  of  the 
base  and  altitude. 

{Altitude  =  V Hypothenuse2  —  Base2. 
Hypothenuse  =  V Base2  +  Altitude2. 
Base  =  V 'Hypothenuse P  —  Altitude2. 

18.  What  is  the  length  of  a  side  of  a  square  field  containing 
21aV  acres. 

19.  The  distance  between  the  diagonal  corners  of  a  square 
field  is  60  rods ;  what  is  its  area  in  acres,  and  what  the  length 
of  a  side  ? 

20.  Find  the  square  root  of  the  product  of  squares  of  11  and  16. 

21.  The  cube  of  3.5  is  the  square  root  of  what  number  ? 

'  22.  A  ladder  20  ft.  long  is  standing  12  ft.  from  the  bottom. 
of  a  house,  and  leaning  against  its  side  4  ft.  below  the  eaves ; 
how  high  is  the  house  ? 

23.  The  entire  area  of  a  cubic  block  is  384  inches ;  what  is 
the  area  and  length  of  a  diagonal  of  one  of  its  faces  ? 

24.  A  telegraph  wire  69  ft.  long  fell  from  the  roof  of  a  house 
36  ft.  high  and  struck  the  opposite  curb  stone;  how  wide  was 
the  street  ? 

25.  What  is  the  length  of  a  diagonal  path  across  a  park 
containing  an  acre  in  the  form  of  a  square  ? 

26.  A  rope  11 6  ft.  long  will  reach  from  a  point  in  the  street 
to  a  window  on  one  side  the  street  35  ft.  high,  and  to  a  window 
on  the  opposite  side  45  ft.  high  i  how  wiete  is  the  street.. 


256 


Powers  and  Moots, 


CUBE     ROOT. 

624.  Extracting  the  Cube  Root  of  a  number  is  finding  one 
of  its  three  equal  factors. 

Boots:     1,  2,    3,     4,      5,       6,       7,       8,       9,       10. 
Cubes:    1,  8,  27,  64,  125,  216,  343,  512,  729,  1000. 

Peikciples. — 1°.  The  cute  of  a  number  cannot  have  more 
than  three  times  as  many  figures  as  its  root,  nor  but  two  less. 

2°.  If  a  number  is  separated  into  periods  of  three  figures  each 
beginning  at  units  place,  the  number  of  figures  in  the  cube  root 
vrill  be  the  same  as  the  number  of  periods. 

625.  To  extract  the  cube  root  of  a  number. 

l.  Find  the  cube  root  of  1860867. 

1860867(123,  Ans. 
1 
102  x  3  = 
10  x  3  x  2  = 
22  = 
1st  Complete  Div., 

1202  x  3  = 
120  x  3  x  3  = 
32  = 
2d  Complete  Div., 


Explanation. — The  cube  of  the  first  period  is  1,  which  is  placed  in  the 
root.  Bringing  down  the  next  period  for  a  dividend,  find  a  trial  divisor 
by  squaring  the  root  already  found  with  a  cipher  annexed,  and  multiply 
this  square  by  3,  the  product,  300,  is  contained  in  800,  two  times.  Write 
2  in  the  root,  and  complete  the  divisor  by  adding  to  it  3  times  the  product 
of  the  root  already  found  with  cipher  annexed,  multiplied  by  the  next 
figure  of  the  root,  making  60,  also  add  the  square  of  this  next  figure. 
The  divisor  completed  is  364.  Multiply  it  by  the  root  figure  and  subtract 
the  product,  the  remainder  is  132.  Bring  down  the  next  period,  and  for  a 
second  trial  divisor,  multiply  the  square  of  the  root  (12)  with  cipher 
annexed,  by  3,  making  43200.  This  is  contained  in  the  dividend  3  times. 
Completing  the  divisor  as  before,  the  root  is  123,  Arts.     Hence,  the 


300 

860 

60 

4 

728 

364 

132867 

43200 

1080 

9 

44289 

132867 

Cube  Moot  257 


General     Rule. 

1.  Separate  the  given  number  into  periods  of  three 
figures  each ;  begin  with  units  and  count  both  ways. 

II.  Find  the  greatest  cube  in  the  first  period  on  the 
left,  and  place  its  root  on  the  right.  Subtract  this  cube 
from  the  period,  and  to  the  right  of  the  remainder 
bring  down  the  next  period  for  a  dividend, 

III.  For  a  trial  divisor,  multiply  the  square  of  the  root 
thus  found,  considered  as  tens,  by  three ;  find  how  many 
times  it  is  contained  in  the  dividend,  and  write  the 
quotient  for  the  second  figure  of  the  root. 

IV.  To  complete  the  trial  divisor,  add  to  it  three  times 
the  product  of  the  root  previously  found  with  a  cipher 
annexed,  by  the  next  root  figure,  also  add  the  square  of 
this  next  figure. 

V.  Multiply  the  divisor  thus  completed  by  the  last 
figure  placed  in  the  root.  Subtract  the  product  from 
the  dividend ;  ami  to  the  right  of  the  remainder  bring 
down  the  next  period  for  a  new  dividend.  Find  a  new 
trial  divisor  as  before,  and  thus  proceed  till  the  root  of 
the  last  period  is  found. 

Notes. — 1.  If  there  is  a  remainder  after  the  root  of  the  last  period  is 
found,  annex  periods  of  ciphers,  and  proceed  as  before.  The  root  figures 
thus  obtained  will  be  decimals. 

2.  If  a  trial  divisor  is  not  contained  in  the  dividend,  put  a  cipher  in 
the  root,  two  ciphers  on  the  right  of  the  divisor,  and  bring  down  the  next 
period. 

3.  If  the  product  of  the  divisor  completed  into  the  figure  last  placed  in 
the  root  exceeds  the  dividend,  the  root  figure  is  too  large.  Sometimes  the 
remainder  is  larger  than  the  divisor  completed ;  but  it  does  not  necessarily 
follow  that  the  root  figure  is  too  small. 

Find  the  cube  root  of  the  following  numbers : 

2.  39304.        5.  109095.488     8.  1.658503. 

3.  104329.        6.  216.68921.      9.  125.000512. 

4.  1.74088.       7.  46268279.     10.  41063625. 


258  Powers  and  Roots. 

626.  To  find  the  cube  root  of  a  common  fraction,  reduce  the 
fraction  to  its  lowest  terms,  then  extract  the  root  of  its  numera- 
tor and  denominator. 

Notes. — 1.  When  either  the  numerator  or  denominator  is  not  a  perfect 
cube,  the  fraction  should  be  reduced  to  a  decimal,  and  the  root  of  the  deci- 
mal be  found  as  above. 

2.  A  mixed  number  should  be  reduced  to  an  improper  fraction. 

11.  What  is  the  cube  root  of  ^^  ? 
Solution. — */$%%  =  |,  Am. 

Find  the  cube  root  of  the  following: 

12.  «f  13.   fffr.  14.  ^f£.  15.  -rHh* 

16.  Extract  the  cube  root  of  the  square  of  999. 

17.  Find  the  fifth  power  of  8  and  extract  its  cube  root. 

18.  What  is  the  inside  measurement  of  a  cubic  box  that 
will  hold  2^  bushels  of  wheat  ? 

19.  What  is  the  side  of  a  cubic  bin  which  may  be  exactly 
filled  by  600  bu.  wheat,  allowing  2150.4  cu.  in.  to  a  bushel  ? 

20.  What  is  the  length  of  one  side  of  a  cubic  cistern  that 
will  hold  160  hogsheads  of  water  ? 

21.  Extract  the  cube  root  of  205692449327. 

22.  If  a  cubical  box  contains  54872  cu.  inches,  what  is  the 
length  of  one  side  ? 

23.  What  is  the  cube  root  of  67917312  ? 

24.  Find  the  cube  root  of  444194947  ? 

SIMILAR     SURFACES     AND     SOLIDS. 

627.  Similar  Surfaces  and  Similar  Solids  are  those  which 
have  the  same  form,  and  their  like  dimensions  proportional 

Notes. — 1.  All  circles  and  all  rectilinear  figures  are  similar,  when  their 
several  angles  are  equal  each  to  each,  and  their  like  dimensions  propor- 
tional. 


Similar  Surfaces  and  Solids.  259 

2.  The  like  dimensions  of  circles  are  their  diameters,  radii,  and  circum- 
ferences. 

3.  The  like  dimensions  of  spheres  are  their  diameters,  radii,  and 
circumferences  ;  those  of  cubes  are  their  sides. 

4.  The  like  dimensions  of  cylinders  and  cones  are  their  altitudes,  and 
the  diameters  or  the  circumferences  of  their  bases. 

5.  Pyramids  are  similar,  when  their  bases  are  similar  polygons,  and 
their  altitudes  proportional. 

G.  Polyhedrons  (£.  e.,  solids  included  by  any  number  of  plane  faces)  are 
similar,  when  they  are  contained  by  the  same  number  of  similar  polygons, 
and  all  their  solid  angles  are  equal  each  to  each. 

628.  Principles. — 1°.  The  Areas  of  similar  surfaces  are  to 
each  other  as  the  squares  of  their  like  dimensions.     Conversely, 

2°.  The  Like  Dimensions  of  similar  surfaces  are  to  each 
other  as  the  square  roots  of  their  areas. 

3°.  The  Contents  of  similar  solids  are  to  each  other  as  the 
cubes  of  their  like  dimensions.     Conversely, 

Jf°.  The  Like  Dimensions  of  similar  solids  are  as  the  cube 
roots  of  their  contents. 

1.  If  one  side  of  a  triangle  is  9  inches,  and  its  area  is  36 
inches,  what  is  the  area  of  a  similar  triangle  the  correspond- 
ing side  of  which  is  18  inches  ? 

Solution.— 92  :  183  : :  36  in.  :  x  in.,  or  144  inches,  Ans. 

2.  The  area  of  a  triangle  is  36  inches,  and  one  side  of  it  is 
9  inches ;  what  is  the  corresponding  side  of  a  similar  triangle 
whose  area  is  144  inches  ? 

Solution.— ^36  :  <\/T44  : :  9  in.  :  x  in.,  or  18  in.,  Ans. 

3.  If  the  area  of  a  triangular  pyramid  is  16  sq.  feet,  and  one 
side  of  the  base  is  20  inches,  what  is  the  area  of  a  similar 
pyramid  the  corresponding  side  of  which  is  30  inches? 

4.  A  quarter  section  of  land  is  160  rods  square ;  what  is  the 
length  of  one  side  of  a  square  tract  containing  36000  acres  ? 

5.  The  area  of  a  triangle  is  206  sq.  inches,  its  altitude  24 
inches  ;  what  is  the  area  of  a  similar  triangle  whose  altitude  is 
56  inches? 


260  Powers  and  Boots. 

6.  If  the  diameter  of  a  circle  is  20  feet,  what  will  be  the 
diameter  of  another  circle  3  times  the  area  of  the  first  ? 

7.  If  a  ball  weighs  40  pounds  whose  diameter,  is  6  inches, 
what  will  a  ball  whose  diameter  is  12  inches  weigh? 

Solution.— 63 :  123  : :  40  lb.  :  x  lb.,  or  320  lb.,  Ana. 

8.  If  a  ball  which  weighs  64  pounds  is  8  inches  in  diameter, 
what  is  the  diameter  of  a  similar  ball  weighing  343  pounds  ? 

Solution.— ^64  lb.  :  /^/343  lb.  : :  8  in.  :  x  in.,  or  14  inches,  Ana. 

9.  If  a  pyramid  20  ft.  high  contains  4600  cu.  ft.,  what  are  the 
cubic  contents  of  a  similar  pyramid  100  ft.  high  ? 

10.  If  a  stack  of  hay  containing  8  cwt.  is  8  ft.  high,  what 
will  be  the  height  of  a  similar  stack  containing  3  tons? 

11.  If  a  cylindrical  cistern  5  feet  in  diameter  contains  65.44 
cubic  feet,  what  will  a  similar  cistern  contain  whose  diameter 
is  20  feet? 

12.  If  an  ox  that  girts  6  feet  weighs  900  pounds,  what  will 
be  the  weight  of  an  ox  that  girts  7  feet  ? 

13.  A  half  peck  measure  is  9J  in.  diameter  and  4  in.  deep  ; 
what  are  the  dimensions  of  a  similar  measure  that  will  hold  a 
bushel  ? 

14.  If  a  cable  2  centims  in  diameter  will  sustain  217 
kilograms,  how  many  kilograms  will  a  cable  9  centims  in 
diameter  sustain  ? 

15.  If  a  ball  5  inches  in  diameter  weighs  75  pounds,  how 
much  will  a  ball  11  inches  in  diameter  weigh  ? 

16.  If  a  globe  5  centimeters  in  diameter  is  worth  $450,  what 
is  the  value  of  a  globe  10  centimeters  in  diameter? 

17.  Two  similar  triangular  fields  contain  respectively  80  and 
90  acres ;  a  side  of  the  former  is  75  rods,  what  is  the  corres- 
ponding side  of  the  latter? 

18.  If  a  pipe  3  centims  in  diameter  fills  a  cistern  in  4  hr. 
16  min.,  what  must  be  the  diameter  of  a  pipe  which  can  fill  it 
in  49  minutes  ? 


ENSURATION. 


19- 


PLANE    FIGURES. 

629.  Mensuration  is  the  process  of  measuring  lines,  sur- 
faces,, and  solids. 

Note. — For  the  measurement  of  rectangular  surfaces  and  solids,  see 
Arts.  165,  179. 

630.  A  Regular  Polygon  has  all  its  sides  and  all  its  angles 
equal. 

631.  A  polygon  having  three  sides  is  called  a  triangle  ;  four 
sides,  a  quadrilateral  j  five  sides,  a  pentagon  ;  six  sides,  a  hex- 
agon ;  seven  sides,  a  heptagon  ;  eight  sides,  an  octagon  ;  etc. 


632.  The  Altitude  of  a  quadrilateral 
having  two  parallel  sides  is  the  perpendic- 
ular distance  between  these  sides  ;  as,  AL. 


633.  The  Diagonal  of  a  figure  is  a  straight  line  AB  which 
joins  the  vertices  of  two  opposite  angles.     (Art.  166.) 


634.  A  Vertical  Line  is  a  right  line  per- 
pendicular to  a  horizontal  line.     (Art.  167.) 

635.  A  Rhomboid  is  an  oblique-angled  par- 
allelogram. 


%> 

* 
j? 


636.  A  Rhombus  is  an  equilateral  rhom- 
boid. 


240 


262 


Mensuration. 


637.  A  Trapezoid  is  a  quadrilateral 
which  has  two  of  its  sides  parallel. 

638.  A  Trapezium  is  a  quadrilateral 
haying  four  unequal  sides,  no  two  of 
which  are  parallel. 

Note. — The  line  AB  is  the  diagonal  of 
the  adjoining  figure. 


639.  A  Triangle  is  a  polygon  haying  three  sides 
and  three  angles. 

640.  The  Base  of  a  triangle  is  the  side  AB  on 

which  it  is  supposed  to  stand. 

ad     a 

641.  A  Vertical  Angle  is  the  angle  opposite  the  base;  as  0. 

642.  An  Equilateral  Triangle  is  one  haying 
three  equal  sides. 

643.  The  Altitude  of  a  triangle  is  the  per- 
pendicular CD  drawn  from  the  vertical  angle 
to  the  base. 


AREA     OF     PLANE    FIGURES. 

644.  The  Area  of  a  plane  figure  is  the  surface  bounded  by 
its  perimeter. 

645.  It  is  proved  by  Geometry  that 

TJie  area  of  a  triangle  is  equal  to  half  the  area  of  a  parallelo- 
gram of  equal  base  and  altitude. 

Illustration. — Let  ABCD  be  a  parallelogram 
whose  altitude  is  the  perpendicular  EB. 

Connect  the  diagonal  corners  by  the  straight 
line  BD,  and  the  parallelogram  will  be  divided 
into  two  equal  triangles,  the  altitude  of  each 
being  EB. 


Area  of  Plane  Figures. 


263 


The  area  of  a  parallelogram  or  rectangle  is  equal  to  the  length  multi- 
plied by  the  breadth.  The  sides  mast  be  reduced  to  the  same  denomina- 
tion before  multiplying. 

Note. — The  perimeter  of  a  parallelogram  of  unequal  sides  is  greater 
than  that  of  a  square  of  equal  area. 

Illustration. — Let  the  adjoining  figure 
be  a  garden  whose  area  is  16  sq.  rods.  If  a 
fence  is  put  around  it  in  its  square  form,  its 
length  will  be  16  rods.  Bat  if  a  the  width  is 
exchanged  for  an  equal  area  in  the  rear,  the 
length  of  the  garden  will  then  be  four  times 
its  width  and  the  length  of  fence  required 
will  be  20  rods. 


4  rods. 

4  x  4  =  16  eq.  rods. 


1.  A  lot  of  ground  80  ft.  long  by 
20  ft.  wide  was  cut  diagonally  by  a 
railroad,  leaving  a  triangular  plot  of  the  same  base  and  altitude; 
what  was  its  area  ? 

2.  What  will  it  cost  to  pave  a  roadway  80  feet  long  and  15 
ft.  wide,  at  $1.50  per  sq.  yard  ? 

3.  What  will  it  cost  to  plaster  a  room  15  ft.  6  in.  long,  13  ft. 
8  in.  wide,  and  9  ft.  high,  at  26  cents  a  square  yard  ? 

4.  Two  fields  contain  10  acres  each ;  one  is  in  the  form  of  a 
square,  the  other  is  4  times  as  long  as  it  is  wide  ;  what  would 
be  the  difference  in  expense  of  fencing  them  at  $2.25  per  rod  ? 

5.  If  the  fence  were  built  4£  ft.  high,  of  boards  8  in.  wide, 
the  lower  one  raised  2  in.  above  the  ground,  and  a  space  of  3 
in.  between  the  boards,  how  many  sq.  feet  of  boards  would  be 
required  for  both  fields  ? 

6.  How  many  more  for  one  than  for  the  other  ? 

7.  A  piece  of  land  containing  2  acres  is  5  times  as  long  as  it 
is  broad ;  what  are  its  length  and  breadth  ? 

8.  How  many  bricks  8  in.  long  and  4  inches  wide  will  pave 
a  yard  that  is  100  ft.  by  50  ? 

9.  How  many  yards  of  carpeting  J  yd.  wide  will  cover  a 
floor  27  ft.  3  in.  long  and  22  ft.  6  in.  wide?  How  many 
breadths  will  it  require  ? 

10.  If  the  room  were  23  ft.  8  in.  wide,  how  much  would  you 
need  to  buy  allowing  for  waste  ? 


264  Mensuration, 


AREA    OF    TRIANG-LES. 

646.  To  find  the  Area  of  a  Triangle,  when  the  Base  and 
Altitude  are  given. 

Multiply  the  base  by  half  the  altitude.     (Art.  632.) 

Note. — Dividing  the  area  of  a  triangle  by  the  altitude  gives  the  base. 
Dividing  the  area  by  half  the  base  gives  the  altitude. 

1.  What  is  the  area  of  a  triangle  whose  base  is  24  feet  and 
altitude  16  feet  ? 

2.  The  base  of  a  triangle  is  28  centimeters  and  the  altitude 
16  centimeters  ;  what  is  the  area? 

3.  A  board  16  feet  long  is  22  inches  wide  at  one  end,  and 
tapers  to  a  point;  what  is  the  value  at  4J  cents  a  sq.  foot  ? 

647.  To  find  the  Area  of  a  Triangle,  when  the  Three  Sides 
are  given. 

From  half  the  sum  of  the  three  sides  subtract  each  side  respec- 
tively ;  then  multiply  half  the  sum  and  the  three  remainders 
together,  and  extract  the  square  root  of  the  product. 

4.  What  is  the  area  of  a  triangle  whose  sides  are  respectively 
12  feet,  16  feet,  and  18  feet  ? 

Solution.—  (12  +  16  +  18)-*-2  =  23 ;  23-12  =  11 ;  23-16  =  7  ;  23-18  = 
5.    And  23  x  11  x  7  x  5  =  8855  ;  ^8855  =  94.1  +  sq.  ft.,  Ana. 

5.  How  many  acres  in  a  triangular  field  whose  sides  are 
respectively  45,  55,  and  60  feet  ? 

6.  What  is  the  area  of  an  equilateral  triangle  whose  side  is 
24  feet  ? 

648.  To  find  the  Altitude,  when  the  Area  and  Base  are  given. 
Eule. — Divide  the  area  by  half  the  base. 

7.  What  is  the  altitude  of  a  triangle  whose  area  is  37J  square 
yards  and  base  5  yards?  Ans.  15  yards. 


Circles.  265 

8.  At  $6.25  a  sq.  rod,  a  triangular  lot  cost  $1281.25 ;  the 
base  was  40  rods,  what  was  the  length  ? 

9.  The  base  of  a  triangle  is  128  ft.,  area  298f  sq.  yd. ;  what 
is  the  altitude  ? 

10.  A  house  lot  containing  12  A.  56  sq.  rods  was  in  the  form 
of  a  triangle,  the  base  of  which  was  56T|T  rods  ;  what  was  the 
altitude  ? 

649.   To  find  the  Base,  when  the  Area  and  Altitude  are  given. 
Kule. — Divide  the  area  by  half  the  altitude. 

11.  What  is  the  base  of  a  triangle  whose  area  is  156  sq.  ft. 
and  its  altitude  12  feet  ?       .  Ans.  26  feet. 

12.  What  is  the  base  of  a  triangle  whose  area  is  144  acres 
and  its  altitude  60  rods  ? 

13.  Find  the  base  of  a  triangle  whose  area  is  5280  sq.  yd., 
and  altitude  240  yards. 

14.  A  garden  contains  -J  of  an  acre  in  shape  of  a  triangle, 
the  altitude  of  which  is  2  rods  4  ft.  3  inches ;  what  is  the 
base  ? 

15.  A  triangular  field  whose  altitude  is  70£  rods,  contains 
12  A.  56  sq.  rods;  what  is  the  base  ? 


CIRCLES. 

650.  A  Circle  is  a  plane  figure  bounded 
by  a  curve  line,  every  part  of  which  is 
equally  distant  from  a  point  within  called 
the  center.  a 

651.  The  Circumference  of  a  circle  is 
the  curve  line  by  which  it  is  bounded. 

652.  The  Diameter  is  a  straight  line  drawn   through  the 
center,  terminating  at  each  end  in  the  circumference,  as  AB. 


266  Mmswratim. 

653.  The  Radius  is  a  straight  line  drawn  from  the  center  to 
the  circumference,  and  is  equal  to  half  the  diameter,  as  CE. 

Note.— From  the  definition  of  a  circle,  it  follows  that  all  the  radii  are 
equal;  also,  that  all  the  diameters  are  equal. 

654.  From  the  relation  of  the  circumference  and  diameter 
to  each  other,  we  derive  from  Geometry  the  following 

Pki^ciples.—  1°.  TJie  Circumference=the  Diameter  x  8.U16 
nearly. 

2°.  The  Diameter  of  a  Circle  =  the  Circumference  -f-  3.1416 
nearly. 

3°.  The  Area  of  a  Circle  =  half  the  Circumference  x  by  the 
Radius. 

Notes. — The  diameter  of  a  circle  may  also  be  found  by  dividing  the 
area  by  .7854  and  extracting  the  square  root  of  the  quotient. 

2.  The  area  of  a  circle  may  also  be  found  by  multiplying  the  square  of 
its  diameter  by  the  decimal  .7854,  or,  by  multiplying  the  circumference  by 
\  the  diameter. 

3.  The  decimal  .7854  is  found  by  taking  \  of  the  area  of  a  circle  whose 
circumference  is  1,  that  is  \-  of  3.1416. 

1.  What  is  the  circumference  of  a  disc  of  15  inches  radius  ? 
Solution.— 15  x  2  x  3.1416  =  94.248  inches,  Ans. 

2.  What  is  the  diameter  of  a  lake  721  r.  in  circumference  ? 
Solution.— 721  rods-s-3.1416  =  229.5+  rods,  Ans. 

3.  What  is  the  area  of  a  race-course  320  rods  in  circum- 
ference ? 

Solution.— 320.0000-4-3.1416  =  101.859  rods  =  diameter, 

Radius  =  50.929,  and  ^  circumference  =  160  rods. 
50.929  x  160  =  8148.64  sq.  rods.,  Ans. 

4.  A  cistern  is  29  feet  8  inches  in  circumference;  what  is  the 
diameter  ? 

5.  What  is  the  difference  in  the  perimeters  of  2  acres  of  land, 
one  a  circle  the  other  a  square  ? 


Circles.  267 

6.  What  is  the  diameter  of  a  circular  piece  of  land  measuring 
4|  acres  ? 

7.  How  many  sq.  feet  in  a  circular  grass  plot  45  feet  in 
diameter  ? 

8.  A  circular  fish-pond  is  850  ft.  in  circumference;  what  is. 
its  area  ? 

9.  The  diameter  of  a  circular  piece  of  land  is  84  feet ;  how 
long  a  fence  will  be  required  to  go  around  it  ? 

io.  A  horse  is  tied  to  a  post  in  a  meadow,  by  a  rope  45|  ft. 
long ;  how  much  ground  can  he  graze  upon  ? 

n.  What  is  the  area  of  a  circle  whose  diameter  is  120  rods? 

12.  What  is  the  diameter  of  a  circle  whose  circumference  is 
94.318  yards  ? 

13.  What  is  the  circumference  of  a  circle  whose  diameter  is 
45  rods?    120  rods? 

14.  How  many  acres  in  a  circular  park  whose  circumference 
is  2  miles  ? 

655.  The  Area  of  a  square  inscribed  within  a  circle,  is 
found  by  taking  twice  the  square  of  its  radius. 

15.  What  is  the  largest  square  stick  of  timber  that  can  be 
cut  from  a  log  36  inches  in  diameter  ?  What  is  the  length  of 
one  side  ? 

Solution.— (18  x  18)  x  2  =  648  sq.  in.  =  Area. 
=  25.45+  in.,  Ans. 


16.  How  large  a  stick  of  square  timber  can  be  made  from  a 
log  20  inches  in  diameter  ? 

17.  The  circumference  of  a  circle  is  3  ft.  4  in. ;  what  is  the 
side  of  a  square  of  equal  area  ? 

18.  What  is  the  difference  between  the  area  of  a  square 
circumscribed  about  a  circle  18  inches  in  diameter,  and  the 
area  of  the  largest  square  that  can  be  inscribed  within  the 
same  circle  ? 

19.  The  circumference. of  a  circle  is  3  meters  4  decimeters; 
what  is  the  area  of  a  square  inscribed  within  it  ? 


268 


Mensuration. 


656.  To  find  the  side  of  a  square  equal  in  area  to  a  given 
circle. 

Rule. — Multiply  the  diameter  by  .8862,  or  the  circum- 
ference by  £821. 

20.  The  diameter  of  a  circle  is  20  feet;  what  is  the  side  of  a 
square  of  equal  area  ? 

Solution.— 20  ft  x  .8862  =  17.7240  feet,  Ana. 

21.  A  field  is  150  rods  in  circumference;  what  is  the  side  of 
a  square  field  of  the  same  area  ? 

22.  The  distance  around  each  of  two  gardens  is  25  rods ;  one 
is  in  the  form  of  a  circle,  the  other  a  square ;  which  contains 
the  more  land,  and  how  much  ? 


SOLIDS. 

657.  A    Solid    is    that    which    has  length,  breadth,   and 
thickness. 

658.  A  Prism  is  a  solid  whose  bases  are 
similar,  equal,  and  parallel,  and  whose  sides 
are  parallelograms. 

Note. — When  their  bases  are  parallelograms  they 
are  called  parallelopipeds,  or  parallelopipedons. 

659.  All  rectangular  solids  are  prisms. 

660.  A  Right  Prism  is  one  whose  sides  are 
perpendicular  to  its  bases. 

661.  A  Rectangular  Prism  is  one  whose  bases  are  rectangles, 
and  its  sides  perpendicular  to  its  bases. 


662.  A  Triangular  Prism  is  one  whose  bases 
are  triangles. 

Notes. — 1.  Prisms  are  named  from  the  form  of  their 
bases,  as  triangular,  quadrangular,  pentagonal,  hexa- 
gonal, etc. 

2.  When  their  sides  are  all  equal  to  each  other  they 
are  called  cubes. 


Solids.  269 

663.  The  Lateral  Surface  of  a  prism  is  the  sum 
of  all  its  faces. 

664.  A  Cylinder  is  a  circular  body  of  uniform 
diameter,  whose  ends  are  equal  parallel  circles. 

665.  The  Altitude  of  a  prism  or  a  cylinder  is 
the  perpendicular  distance  between  its  bases. 

666.  To  find  the  Lateral  Surface  of  a  Prism  or  Cylinder. 

Eule. — Multiply  the  perimeter  of  the  base  by  the 
altitude. 

Note. — To  find  the  entire  surface,  the  area  of  the  bases  must  be  added 
to  the  lateral  surface. 

1.  What  is  the  lateral  surface  of  a  prism,  the  altitude  of 
which  is  18  feet  and  its  base  a  pentagon,  each  side  of  which  is 
8  feet. 

Solution.— 8  ft.  x  5  =  40  ft.  the  perimeter. 

40  ft.  x  18  =  720  square  feet,  the  surface,  Ans. 

2.  What  is  the  convex  surface  of  a  cylinder  the  circumfer- 
ence of  whose  base  is  62  inches,  and  the  altitude  3  feet? 

Solution.— 62  in.  x  36  =  2232  sq.  inches,  Ans. 

3.  How  many  square  feet  of  canvas  will  be  required  to 
cover  a  cylinder  16£  feet  in  circumference  and  25  feet 
long? 

4.  How  many  square  feet  of  surface  m  a  stove  pipe  22  inches 
in  circumference  and  12  feet  long  ? 

5.  What  is  the  convex  surface  of  a  log  25  ft.  in  circumfer- 
ence and  18  ft.  long  ? 

6.  What  is  the  convex  surface  of  a  cylinder  3  ft.  long  and 
1\  ft.  in  diameter?    What  is  its  entire  surface  ? 


270  Mensuration. 

667.  To  find  the  Contents  of  a  Prism  or  Cylinder,  when  the 
Perimeter  of  the  Base  and  the  Altitude  are  given. 

Rule. — Multiply  the  area  of  the  base  by  the  altitude. 

Note. — This  rule  is  applicable  to  all  prisma,  triangular,  quadrangular, 
etc.  ;  also  to  all  parallelopipedons. 

7.  The  standard  bushel  of  the  United  States  is  18J  inches 
in  diameter  and  8  inches  deep  ;  how  many  cubic  inches  does  it 
contain  ? 

Solution.— The  diam.  18^  in.  x  3.1416  =  58.1196  in.  =  circumference. 
58.1196^-2  =  29.0598  ;  and  18|-*-2  =  9}  ; 
29.0598  x  9i  =  268.8031  sq.  in.  =  area. 
And  268.8031  x  8  =  2150.4248  cu.  in.,  Am. 

8.  What  are  the  contents  of  a  log  15  ft.  long  and  2  ft.  in 
diameter  ? 

9.  The  standard  liquid  gallon  is  231  cubic  inches;  how 
many  gallons  in  a  can  22  inches  in  diameter  and  3  feet  high  ? 

10.  How  many  en.  feet  in  a  triangular  prism,  the  area  of 
whose  base  is  920  square  feet  and  height  20  feet  ? 

11.  What  are  the  contents  of  a  quadrangular  prism  whose 
length  is  25  centimeters,  and  the  base  a  rectangle  3  by  5 
centimeters  ? 

12.  How  many  liters  will  fill  a  cistern  2  meters  long,  5  decims 
wide,  and  8  decims  deep  ?    How  many  kiloliters  of  water  ? 

13.  What  are  the  contents  of  a  triangular  prism,  each  side 
of  which  is  30  inches  wide  and  5  feet  long  ? 


Fyramicl,  Frustum.  Coue.  Frustum 


Solids.  271 

668.  A  Pyramid  is  a  solid  whose  base  is  a  triangle,  square, 
or  poly y 07i,  and  whose  sides  terminate  in  a  point,  called  the 
vertex. 

Note. — The  sides  which  meet  in  the  vertex  are  triangles. 

669.  A  Cone  is  a  solid  which  has  a  circle  for  its  base,  and 
terminates  in  a  point  called  the  vertex. 

670.  The  Altitude  of  a  pyramid  or  a  cone  is  the  perpen- 
dicular distance  from  the  base  to  the  vertex. 

671.  The  Slant  Height  of  a  pyramid  is  the  distance  from 
the  middle  of  any  side  of  the  base  to  the  vertex. 

672.  A  Frustum  of  a  pyramid  or  cone  is  the  part  which  is 
left  after  the  top  is  cut  off  by  a  plane  parallel  to  the  base. 

673.  To  find  the  Lateral  or  Convex  Surface  of  a  Regular 
Pyramid  or  Cone. 

Eule. — Multiply  the  perimeter  of  the  base  by  £  the 
slant  height. 

To  find  the  entire  surface,  Add  the  area,  of  the  base  to  the 
convex  surface. 

14.  What  is  the  lateral  surface  of  a  regular  pyramid  whose 
slant  height  is  15  ft,  and  the  base  is  30  ft.  square? 

Solution.— Perimeter  of  base  =  30  x  4  =  120  ft. 

120  x  7|  (|  slant  height)  =  900  sq.  ft.,  Arts. 

15.  What  is  the  surface  of  a  pyramid  whose  base  is  an 
equilateral  triangle  measuring  4  ft.  on  each  side,  and  slant 
height  16  feet  ? 

16.  What  is  the  convex  surface  of  a  cone,  the  diameter  of 
whose  base  is  7  ft.  and  its  altitude  12  feet  ? 

17.  What  is  the  entire  surface  of  a  triangular  pyramid  whose 
slant  height  is  25  feet,  and  each  side  of  the  base  10  feet. 

18.  What  is  the  entire  surface  of  a  right  cone,  the  diameter 
pf  the  base  and  the  slant  height  being  each  40  feet  ? 


272 


Mensuration. 


674.  To  find  the  Contents  of  a  Pyramid  op  a  Cone,  when  the 
Base  and  Altitude  are  given. 

Kule. — Multiply  the  area  of  base    by    %  the  altitude. 

Note.— The  contents  of  a  frustum  of  a  pyramid  or  cone  are  found  by 
adding  the  areas  of  the  two  ends  to  the  square  root  of  the  product  of  those 
areas,  and  multiplying  the  sum  by  ^  of  the  altitude. 

19.  What  are  the  contents  of  a  pyramid  whose  base  is  144  sq. 
feet,  and  its  altitude  33  feet  ? 

Solution. — 144  sq.  ft.  x  11  (|  of  altitude)  =  1584  cu.  ft.,  Ans. 

20.  What  are  the  contents  of  a  cone  the  area  of  whose  base 
is  1865  sq.  feet,  and  its  altitude  36  feet? 

Solution.— 1865  x  12  ft  of  altitude)  =  22380  cu.  ft. 

21.  A  monument  in  the  form  of  a  square  pyramid,  is  2  ft. 
10  in.  square  at  base,  and  11  ft.  high;  at  175  lb.  to  a  cu.  ft. 
what  is  its  weight  ? 

22.  What  are  the  contents  of  a  round  log  whose  length  is 
20  ft.,  diameter  of  larger  end  12  in.,  and  smaller  end  6  inches  ? 

23.  The  altitude  of  a  frustum  of  a  pyramid  is  27  ft.,  the  ends 
are  4  ft.  and  3  ft.  square ;  what  is  its  solidity  ? 


675.  A  Sphere  or  Globe  is  a  solid  ter- 
minated by  a  curve  surface,  every  part  of 
which  is  equally  distant  from  a  point 
within,  called  the  center. 

676.  The  Diameter  of  a  sphere  is  a 
straight  line  drawn  through  its  center 
and  terminated  afc  both  ends  by  the 
surface. 

677.  A  Hemisphere  is  one-half  a  sphere. 


678.  The  Radius  of  a  sphere  is  a  straight  line  drawn  from 
its  center  to  any  point  in  its  surface. 


Gauging  of  Casks.  273 

679.  To  find  the  Surface  of  a  Sphere,  the  Circumference  and 
Diameter  being  given. 

Eule. — Multiply  the  circumference  by  the  diameter. 

24.  Require  the  surface  of  a  globe  4  inches  in  diameter. 

Solution.— 4x3.1416  =  12.5664  in  circumference. 

12.5654  x  4  =  50.2656  sq.  in.  surface,  Ans. 

25.  What  will  it  cost  to  gild  a  ball  12  inches  in  diameter,  at 
10  cents  a  square  inch  ? 

26.  Required  the  surface  of  the  earth,  its  diameter  being 
8000  miles. 

27.  The  diameter  of  a  sphere  is  100  centimeters;  what  is  its 
surface  ? 

680.  To    find    the    Solidity   of  a   Sphere,    the  Surface  and 
Diameter  being  given. 

Rule. — Multiply  the  surface  by  £  of  the  diameter. 

28.  Find  the  solidity  of  a  sphere  whose  diameter  is  12  inches 
and  its  surface  4.91  sq.  feet  ? 

Solution. — 4.91  x  144  ■=  707.04  sq.  in.  surface. 

707.04  sq.  in.  x  2  =  1414.08  cu.  in.,  Ans. 

29.  What  is  the   solidity  of  the  earth,  its  surface  being 
196900278  sq.  miles,  and  its  mean  diameter  7916  miles  ? 

30.  Find  the   solidity  of  a  cannon   ball  3   decimeters  in 
diameter  ? 

31.  The  basin  of  a  fountain  is  a  hemisphere  22-|  ft.  in 
diameter;  what  are  its  cubical  contents  ? 

32.  How  many  hogsheads  of  water  will  it  contain  ? 

GAUGING    OF    CASKS. 

681.  Gauging  is  finding  the  capacity  or  contents  of  casks 
and  other  vessels. 

682.  The  mean  diameter  of  a  cask  is  equal  to  half  the  sum 
of  the  head  diameter  and  bung  diameter.     (Art.  339.) 


274  Mensw*ation. 

Note.— The  contents  of  a  cask  are  equal  to  those  of  a  cylinder  having 
the  same  length  and  a  diameter  equal  to  the  mean  diameter  of  the  cask. 

683.  To  find  the  Contents  of  a  Cask,  when  its  Length,  its 
Head,  and  Bung  Diameters  are  given. 

Rule. — Multiply  the  square  of  the  mean  diameter  by 
the  length  in  inches,  and  this  product  by  .0034  for 
gallons,  or  by  .0129  for  liters. 

Note. — In  finding  the  contents  of  cisterns,  it  is  sufficiently  accurate  for 
ordinary  purposes  to  call  a  cubic  foot  =  7$  gallons. 

1.  How  many  gallons  in  a  cask  whose  length  is  35  inches,  its 
bung  diameter  30  inches,  and  head  diameter  26  inches? 

Solution.— (30 +  26) -4- 2  =  28  in.,  the  mean  diameter.     (Art.  682.) 

282  x  .7854  =  area  of  base. 

Area  of  base  x  length  =  contents  in  cubic  inches,  which  are  reduced  to 
gallons  by  dividing  by  231. 

Instead  of  using  the  factor  .7854,  if  we  divide  it  by  231,  the  number  of 
cubic  inches  in  a  gallon,  and  multiply  by  the  quotient  .0034,  the  operation 
is  shortened,  and  the  result  is  in  gallons.     Thus, 

282  x  35  x  .0034  =  93.296  gal.,  Ans. 

2.  What  is  the  capacity  in  gallons  of  a  cask  whose  length  is 
26  inches,  its  head  diameter  17,  and  bung  diameter  22  inches  ? 

3.  Find  the  contents  in  liters  of  a  cask  whose  length  is 
54  inches,  its  bung  diameter  42,  and  head  diameter  36  inches  ? 

4.  Required  the  contents  in  gallons  of  a  rectangular  cistern 
4£  ft.  long,  3J  ft.  wide,  and  6  ft.  deep. 

6.  What  are  the  contents  in  gallons  of  a  cask  36  in.  long,  its 
head  diameter  26  inches,  and  bung  diameter  32  inches? 

6.  What  will  be  the  cost  at  60  cents  a  gallon  of  a  cask  of 
molasses,  whose,  length  is  16  in.,  the  head  and  bung  diameters 
10  and  12  inches  ? 

7.  A  cylindrical  ash-receiver  is  18  inches  in  diameter  and  28 
inches  high  ;  how  many  bushels  will  it  contain? 

8.  What  must  be  the  depth  of  a  cylindrical  measure  18| 
inches  in  diameter  to  contain  a  bushel  ? 


Tonnage  of  Vessels.  275 


TONNAGE     OF    VESSELS. 

684.  Tonnage  is  the  weight  in  tons  which  a  vessel  will  carry 
It  is  estimated  by  the  following 

Carpenter's     Rule. 

Multiply  together  the  length  of  the  keel,  the  breadth  at 
the  main  beam,  and  the  depth  of  the  hold  in  feet,  and 
divide  the  product  by  95  (the  cu.  ft.  allowed  for  a,  ton) ; 
the  result  will  be  the  tonnage. 

For  a  double  decker,  instead  of  the  depth  of  the  hold, 
take  half  the  breadth  of  the  beam. 

Note. — A  Register  Ton  =  100  cu.  ft.  is  the  legal  standard. 

*  m.     •      m  J  40  cu.  ft,  U.  S.,  or  )        ",.        A.      u 

A  Shipping  Ton  =  1  .  >  used  in  estimating  cargoes. 

1.  What  is  the  tonnage  of  a  double  decker  with  300  ft.  keel 
and  42  ft.  beam  ?  Ans.  2785^  tons. 

2.  What  is  the  tonnage  of  a  single  decked  vessel  whose 
length  is  150  ft,  the  breadth  30  ft.,  and  the  depth  12  ft? 

Rules  for  the  Measurement  of  Grain. 

685.  To  estimate  the  quantity  of  grain  heaped  in  conical  form 
on  the  floor. 

Rule. — Square  the  depth  and  the  slant  height  in 
inches,  multiply  the  difference  of  the  squares  by  the 
depth,  and  multiply  this  product  by  .0005 ;  the  result  is 
the  contents  in  bushels. 

Note. — When  heaped  against  a  straight  wall,  take  one-half  the  product 
before  multiplying  by  the  decimal. 

3.  A  conical  heap  of  grain  left  by  a  thrashing-machine  was 
5-J-  ft.  high,  and  the  slant  height  was  9  ft.  ;  how  many  bushels 
did  it  contain  ? 

4.  A  quantity  of  wheat  heaped  against  a  straight  wall  was 
4  ft.  high,  and  its  slant  height  was  7  ft. ;  how  many  bushels 
were  there  ? 


276  Mensuration. 

5.  A  quantity  of  grain  was  heaped  in  a  conical  form  in  a 
corner,  perpendicular  height  4  ft.  3  in.,  slant  height  7  ft.  1  in. ; 
what  is  its  value,  at  $1.66|  a  bushel? 

686.   To  measure  the  height  of  an  object  standing  in  a  plane. 

6.  What  is  the  height  of  a  tree  standing  in  a  plane  which 
casts  a  shadow  50  feet,  measured  with  a  pole  5  ft.  long,  casting 
a  shadow  10  ft.? 

Solution. — Take  a  pole  of  any  convenient  length,  and  placing  it  in  a 
perpendicular  position,  measure  the  length  of  its  shadow,  which  we  will 
suppose  to  be  10  feet,  then  by  Proportion 

10  ft.  (shadow  of  p.)  :  50  ft.  (shadow  of  t.)  : :  5  ft.  (1.  of  p.)  :  height  of  tree. 

50  x  5  =  250,  and  250^-10  =  25  feet,  Am. 

7.  What  is  the  height  of  a  pyramid,  standing  in  a  plane, 
which  casts  a  shadow  of  100  feet,  measured  with  a  pole  7-J  ft. 
long  which  casts  a  shadow  of  15  feet  ? 

8.  The  shadow  of  a  tower  was  36f  ft.,  and  that  of  a  cane  2| 
ft.  high  standing  near  it  was  at  the  same  hour  9  inches ;  what 
was  the  height  of  the  tower  ? 


LUMBER 

687.  Doyle's  Rule  for  finding  the  number  of  square  feet  of 
boards  a  round  log  will  yield : 

For  logs  16  feet  in  length,  Subtract  Jf  from  the  diameter 
in  inches  ;  the  square  of  the  remainder  will  be  the  num- 
ber of  square  feet  of  inch  boards  the  log  will  yield  to  each 
16  feet. 

l.  How  much  square-edged  inch  lumber  can  be  cut  from  a 
log  24  inches  in  diameter  and  12  ft.  long. 

Solution.— 24-4  =  20,  202  =  400  sq.  ft.;  12  ft.  =  |f  =  f  of  16  ft. 
'       400  x  |  =  300  sq.  feet.,  Ant. 

Note. — This  rule  is  not  accurate  for  perfectly  straight  logs,  but  gives 
a  sufficiently  just  approximation  for  the  average,  and  is  much  used  by 
lumbermen  on  account  of  its  simplicity. 


lAumber.  277 

2.  How  many  square  feet  of  boards  will  a  log  yield  which  is 
36  iuches  in  diameter  and  18  feet  long? 

3.  How  many  sq.  feet  of  boards  can  be  cut  from  a  log  24 
feet  long  and  18  in.  diameter  ? 

4.  How  many  from  a  log  18  ft.  long  and  12  ft.  diameter  ? 

688.  To  find  the  number  of  inch  boards  which  a  given  thick- 
ness of  log  will  yield. 

Eule. — Divide  the  thickness  of  the  log,  less  \  inch,  by 
1{  inch. 

5.  How  many  boards  may  be  cut  from  a  log  17{  in.  thick  ? 
Solution.— 17£  in  —  \  in.  =  17f  in.     17f-t*l£  =  14  boards,  Ans. 

6.  How  many  boards  may  be  made  from  a  log  16^  in.  thick? 

7.  How  many  square-edged  boards  of  equal  width  can  be 
made  from  a  log  18  ft.  long  and  1G  inches  in  diameter,  allowing 
J  inch  for  saw  cut,  and  what  would  be  the  board  measure  of  the 
whole  ? 

689.  To  find  the  cubic  feet  in  round  timber. 

Eule. — Square  {  the  mean  girt  in  inches,  multiply 
it  by  the  length  in  feet,  and  divide  the  product  by 

Note. — This  rule  only  approximates  the  exact  quantity,  something 
being  allowed  for  crooks  and  waste. 

8.  The  mean  girt  of  a  log  is  36  in.,  its  length  40  ft.;  what  are 
its  contents  in  cubic  feet  ? 

9.  How  many  cu.  ft.  of  timber  in  a  log  26  ft.  long,  and  whose 
mean  girt  is  48  inches  ? 

Note. — The  size  of  square  timber  that  a  log  will  yield  may  be  found 
by  multiplying  the  diameter  of  the  smaller  end  by  .707. 

10.  The  diameter  of  the  smaller  end  of  a  log  is  18  inches ; 
what  is  the  width  of  the  square  timber  that  may  be  sawed 
from  it  ? 


TJESTIONS 


FOR    REVIEW. 

690.  l.  Add  seven  hundred  thousand  two  hundred  sixty, 
twelve  million  twelve,  fifty-four  thousand  four  hundred,  six 
million  two  thousand  twenty-seven. 

2.  From  the  above  sum  subtract  three  million  sixty-five 
thousand  three,  minus  six  hundred  thirty-eight  thousand  four 
hundred  nineteen. 

3.  Add  eighty-four  million  fifteen,  sixty-seven  thousand 
sixty-eight,  five  million  ten  thousand  seventeen,  three  hun- 
dred thousand  twenty,  three  million  eight  thousand  seventy- 
five,  nine  hundred  million  twenty-seven. 

4.  (8143 +  24429) -^-34  x  12  =  what? 

5.  A  lady  went  shopping  with  $15.50  in  her  purse ;  she  paid 
28  cents  for  needles,  $2.25  for  gloves,  $5.75  for  a  dress,  and 
$2.25  for  ribbon  ;  how  much  money  had  she  left? 

6.  If  the  divisor  is  19,  the  quotient  37,  and  the  remainder  11, 
what  is  the  dividend  ? 

7.  A>  person  owning  f  of  a  mine  sold  f  of  his  interest  for 
$1710 ;  what  was  the  whole  mine  worth  ? 

8.  A  market  woman  having  eggs  for  sale,  counted  her  stock 
and  found  that  T\  of  them  made  147  ;  how  many  had  she  ? 

9.  In  a  certain  battle  f  of  the  forces  were  lost,  and  there 
were  9800  men  left ;  how  many  were  there  at  first  ? 

10.  If  |  of  f  of  a  ship  is  worth  $9370,  what  is  the  whole 
worth  ? 

11.  What  is  the  quotient  of  65  bu.  1  pk.  3  qt.,  divided  by  12? 

12.  How  many  bushels  will  a  box  8  ft.  long,  4  ft.  wide,  and 
3  ft.  high  contain  ? 


Test  Questions  for  Review.  279 

13.  One  factor  of  a  number  is  11,  the  other  3708311605 ; 
what  is  the  number  ? 

14.  If  the  quotient  is  610,  the  remainder  17,  and  the  dividend 
45767,  what  is  the  divisor  ? 

*     15.  Find  the  g.  c.  d.  of  192,  744,  and  1044. 

16.  The  sum  of  two  numbers  is  143J,  their  difference  17J ; 
what  are  the  numbers  ? 

17.  Find  the  sum,  difference,  product,  and  quotient  of  -J 
and  -|. 

18.  What  number  multiplied  by  \  of  itself  will  produce  12£? 

19.  A  man  paid  $275  for  a  horse,  which  cost  |  as  much  as 
his  carriage ;  what  did  he  pay  for  the  carriage  ? 

20.  At  $7f  a  barrel,  how  many  barrels  of  flour  must  be  given 
for  530  barrels  of  potatoes  worth  %Z\  a  barrel  ? 

21.  Bought  a  sleigh  for  $75,  which  was  f  of  3  times  the  price 
of  the  harness;  what  was  the  price  of  the  harness? 

22.  A  man  paid  $40  cash  for  a  cow  and  sold  her  at  a  credit 
of  8  months  for  $45;  how  much  did  he  gain,  reckoning  interest 
at  6%? 

23.  How  many  planks  18  ft.  long  and  15  inches  wide,  will 
be  needed  to  floor  a  barn  63£  ft.  long  and  33£  wide  ? 

24.  A  man's  salary  this  year  is  $600,  which  is  J  more  than 
it  was  last  year;  what  was  it  last  year  ? 

25.  If  a  pipe  of  5  inches  diameter  will  discharge  a  cistern  in 
12  hours,  in  what  time  will  a  3-inch  pipe  discharge  it  ? 

26.  A  broken  tree  rested  on  the  stump  20  ft.  from  the  ground, 
and  its  top  touched  the  ground  50  ft.  from  the  stump ;  how 
high  was  the  tree  ? 

•27.  What  is  the  length  of  a  diagonal  drawn  on  the  floor  of  a 
room  30  ft.  long  and  24  ft.  wide  ? 

28.  A  man  sold  his  horse  for  $100  and  gained  25%;  what 
per  cent  would  he  have  gained  if  he  had  sold  at  $120  ? 

29.  What  cost  six  $500  U.  S.  6%  currency  bonds,  at  22£% 
premium  ? 


280  Test  Questions  for  Heview. 

30.  Three  men  hired  a  pasture  for  $150  ;  A  pastured  4  cows 
12  weeks,  B  6  cows  10  weeks,  and  0  8  cows  15  weeks ;  how 
much  should  each  pay  ? 

31.  In  a  school  of  280  pupils,  12  were  absent ;  what  was  the 
per  cent  of  attendance  ? 

32.  A  market  woman  bought  150  oranges  at  the  rate  of  5 
for  2  cts.,  and  sold  %  of  them  at  the  rate  of  3  for  1  ct.,  and  the 
remainder  at  the  rate  of  2  for  1  ct. ;  did  she  gain  or  lose,  and 
how  much  ? 

33.  If  1^-  pounds  of  beef  and  1-^-  pounds  of  flour  are  allowed 
for  a  ration,  how  much  will  560  rations  cost  if  the  price  of 
beef  is  llf  cts.  and  of  flour  3J  cts.  per  pound  ? 

34.  How  many  hektars  of  land  can  a  man  buy  for  $946,  if 
he  pays  at  the  rate  of  $86  for  every  7  hektars  ? 

35.  When  brooms  are  sold  at  $3 £  per  doz.,  what  will  be  the 
cost  of  16|  gross  sold  at  5%  discount  on  bills  over  $100  ? 

36.  If  the  interest  of  $1800  for  12  mo.  is  $108,  what  will  be 
the  interest  of  the  same  sum  for  8  mo.  ? 

37.  If  a  tree  50  ft.  high  casts  a  shadow  60  ft.  long,  how  long 
will  be  the  shadow  of  a  tree  80  ft.  high  ? 

38.  A  number  diminished  by  J  of  itself  is  1140  ;  what  is  the 
number  ? 

39.  What  is  the  sum,  difference,  product,  and  quotient  of 
263|,  and  175f  ? 

40.  A  retail  dealer's  profits  this  year  are  $8350,  which  is  ^ 
less  than  last  year ;  what  were  they  last  year  ? 

41.  The  wholesale  price  of  Grammars  is  98  cents  apiece  ;  but 
for  cash  they  are  J  less ;  what  is  the  cash  price  ? 

42.  A  merchant  fails  for  $12575,  and  his  assets  are  $7500. 
What  per  cent  of  his  debts  can  he  pay  ? 

43.  What  is  the  value  of  a  house  which  brings  $11,500  when 
sold  at  a  loss  of  7£  per  cent.  ? 

44.  If  on  the  day  of  the  battle  of  Lexington  1  cent  had  been 
placed  at  compound  interest  at  6%,  what  would  have  been  the 
amount  on  the  19th  of  April,  1884  ? 


Test  Questions  for  Review.  281 

45.  How  much  do  I  gain  or  lose  if  I  obtain  at  a  bank  $1000 
for  1  year  at  6%  discount,  and  then  put  it  at  interest  for  the 
same  time  and  rate  ? 

46.  The  average  quantity  of  wheat  required  to  make  a  barrel 
of  flour  is  4^  bushels ;  the  cost  of  conversion  is*  56  cts.  a  barrel. 
If  wheat  in  Chicago  is  98J  cts.  a  bushel,  and  expense  of  trans- 
portation 15  cts.  a  bu.,  what  would  be  the  profit  to  a  New 
York  miller  if  8500  bu.  were  sent  from  Chicago,  and  sold, 
when  converted  into  flour,  for  $8 \  a  barrel  ? 

47.  How  many  bushels  of  grain  are  in  a  conical  pile  5  ft. 
high  and  26  ft.  in  circumference  ? 

48.  How  many  bushels  of  wheat  can  be  placed  in  a  car  20  ft. 
long,  8  ft.  wide,  and  7  ft.  high  ? 

49.  How  many  such  cars  would  be  required  to  transport 
8700  bushels  ? 

50.  Two  city  lots  are  sold  at  $2500  each.  How  much  is 
made  or  lost  if  one  is  sold  at  a  profit  of  15  per  cent  and  the 
other  at  a  loss  of  15  per  cent  ? 

51.  What  is  the  exact  interest  on  a  note  of  $1175  from 
September  12th  to  December  24  ? 

52.  At  a  recent  examination  a  student  received  83  per  cent 
in  History,  94  in  Algebra,  and  87  in  Philosophy  ;  what  was 
his  average  per  cent  ? 

53.  A  man  having  4  tracts  of  land  containing  respectively 
175  acres,  210  acres,  318  acres,  and  268  acres,  divided  it  into 
4  farms  ;  what  was  the  average  number  of  acres  in  each  ? 

54.  The  population  of  New  York  and  Philadelphia  together 
in  1880  was  2053469,  the  difference  was  359129  ;  what  was  the 
population  of  each  city  ? 

55.  How  many  centars  in  a  piece  of  land  145  meters  long, 
and  23.2  meters  wide  ? 

56.  How  many  square  feet  of  glass  in  8  windows  of  12  panes 
each,  size  10  in.  by  14  ? 

57.  If  a  staff  3  ft.  8  in.  long  cast  a  shadow  2  ft.  6  in.,  what  is 
the  height  of  a  steeple  that  casts  a  shadow  of  248  ft.  at  the  same 
hour? 


282  Test  Questions  for  Review. 

58.  What  are  the  proceeds  of  a  note  for  $750,  discounted  at 
a  bank  for  30  days  at  6  per  cent  ? 

59.  A  R.  R.  Co.  declared  a  scrip  dividend  of  6%;  to  how 
many  shares  was  a  stockholder  entitled,  who  held  50  shares  of 
the  original  stock  ? 

60.  Sold  at  wholesale  a  bill  of  merchandise  at  25%  discount, 
and  h%  off  for  cash ;  what  was  the  whole  discount  ? 

61.  What  is  the  length  of  a  rope  extending  from  the  top  of 
a  stake  13  ft.  high  to  the  top  of  a  pole  40  ft.  high,  standing 
35  ft.  from  the  stake  ? 

62.  A  merchant  increased  his  capital  the  first  year  by  \  of 
itself,  the  second  year  by  -f ,  the  third  year  he  lost  -f  of  all  he 
had,  and  had  $15000  remaining  ;  what  was  his  capital  at  first? 

63.  What  per  cent  of  an  acre  is  1  sq.  yard  ? 

64.  What  part  of  8  square  feet  is  2  feet  square  ? 

65.  How  many  cu.  meters  in  a  wall  24  meters  long,  8 -fa  m. 
high,  and  52  cm.  thick  ? 

66.  What  would  be  the  cost  of  building  this  wall  is  $4.25 
per  cu.  meter  ? 

67.  If  a  cistern  19J  ft.  long,  10J  ft.  wide,  and  12  ft.  deep, 
hold  546  barrels,  how  many  barrels  will  a  cistern  hold  that  is 
18  ft.  long,  9  ft.  wide,  and  15  ft.  deep? 

68.  If  $500  is  deposited  for  a  child  at  birth,  at  1%  compound 
interest  payable  semi-annually,  what  will  it  amount  to  when 
the  child  is  21  years  old  ? 

69.  The  following  payments  have  been  made  on  a  note  of 
$10000  given  March  1st:  April  3d,  $200;  April  25th,  $10; 
May  20th,  $3000;  July  1st,  $400;  December  15th,  $4000. 
How  much  will  settle  the  note  January  1st  ? 

70.  What  must  be  the  inside  diameter  of  a  globe  that  will 
contain  5  gallons  of  water  ? 

71.  If  a  measure  60  centimeters  deep  holds  a  hektoliter, 
what  is  the  depth  of  a  similar  measure  holding  a  centiliter? 

72.  A  man  owes  $2400,  \  of  which  is  now  due,  \  of  it  in  3 
months,  \  of  it  in  4  months,  and  the  remainder  in  6  months; 
what  is  the  equated  time  of  payment  ? 


Test  Questions  for  Review.  283 

73.  What  is  the  g.  c.  d.  of  529,  782,  and  1127  ? 

74.  For  what  amount  must  a  60-day  note  be  written  to  yield 
$250,  when  discounted  at  a  bank  ? 

75.  If  a  ball  2  inches  in  diameter  weighs  4  pounds,  what  is 
the  weight  of  a  ball  6  inches  in  diameter  ? 

76.  A  piece  of  cloth  of  14  yd.  sold  for  $61.25,  which  was  a 
gain  of  25%  ;  what  was  the  cost  per  yard  ? 

77.  What  is  the  g.  c.  d.  of  1177,  1819,  2782,  and  4708? 

78.  A  gentleman  has  a  note  due  at  bank  on  which  he 
received  $575  for  3  mo.  at  4%  discount ;  he  goes  to  another 
bank  and  obtains  the  money  to  take  up  the  note,  for  which  he 
pays  6%  for  6  mo. ;  what  was  the  face  of  the  last  named  note  ? 

79.  What  are  the  contents  of  a  sphere,  diameter  60  inches  ? 

80.  How  many  hektars  in  a  piece  of  land  -|  mile  square  ? 

81.  How  many  hektoliters  in  a  box,  length  2.25  m.,  width 
1.75  m.,  depth  1  meter  ? 

82.  What  annuity  at  6%  compound  interest  will  amount  to 
$10000  in  20  years? 

83.  What  must  be  the  diameter  of  a  cylindrical  cup  6  in. 
high,  to  hold  a  gallon  ? 

84.  If  a  stock  is  bought  at  109J  and  an  annual  dividend  of 
7%  received,  what  per  cent  is*that  on  the  investment  ? 

85.  A  draft  on  New  Orleans  bought  at  \%  premium  for 
$12000,  was  sent  to  an  agent  to  pay  for  cotton  purchased  at 
1\%  commission ;  what  was  the  value  of  the  cotton  ? 

86.  Find  the  amount  of  duty  on  the  following:  8  casks 
raisins,  at  11  cts.  a  lb.,  gross  weight  888  lb.,  tare  12  lb.  per 
cask,  duty  25$  ad  valorem ;  12  boxes  sugar,  400  lb.  each,  at 
7  cts.  per  lb.,  tare  10%,  duty  24%  ad  valorem ;  60  hhd.  molasses, 
at  54  cts.  per  gal.,  leakage  2%,  duty  20$. 

87.  Mr.  A.  deposits  $20  twice  each  year,  1st  of  Jan.  and 
July,  in  a  savings  bank  which  pays  5%  per  annum,  adding 
the  accrued  interest  at  the  end  of  each  6  months;  what  sum 
will  stand  to  his  credit  in  the  bank  on  the  day  after  he  makes 
his  sixth  deposit  ? 


284  Test  Questions  for  Review. 

88.  If  it  cost  $312  to  enclose  a  field  216  rods  long  and  24 
rods  wide,  what  will  it  cost  to  enclose  a  square  field  of  equal 
area  with  the  same  kind  of  fence  ? 

89.  Three  notes  bearing  interest  are  dated  respectively  July 
3,  1883,  Oct.  9,  1883,  and  Feb.  6,  1884 ;  if  a  single  note  were 
substituted  for  the  three,  what  should  be  its  date  ? 

90.  Ralston  &  Baxter  received  a  consignment  of  8500  bu. 
wheat  from  Jones  &  Co.,  Milwaukee.  Their  account  sales  is  as 
follows:  Oct.  20,  1883,  to  C.  &  Co.  2500  bu.,  at  $1.12  on  30  d.; 
Oct.  22,  to  D.  &  Co.  2500  bu.,  at  $1.11  J  on  10  d. ;  Nov.  1, 
3000  bu.  to  J.  &  Co.,  at  $1.10  on  60  d.;  Nov.  12,  500  bu.  to 
R,  &  Co.,  at  $1.15  on  30  d.  Charges  Oct.  15:  Freight  on 
8500  bu.,  at.l2|;  weighing,  $42.50;  towing,  $14;  demurrage, 
$10  ;  commission,  2 \%.  What  is  the  equated  time  for  the  pay- 
ment of  the  net  proceeds,  the  commission  being  due  at  average 
due  date  of  sales  ? 

91.  What  is  the  present  worth  of  a  reversionary  lease  of  $250, 
which  begins  in  12  years,  and  continues  25  years  at  5%,  com- 
pound interest  ? 

92.  A  man  wishes  to  inclose  a  garden  56J  feet  long  and  40^ 
ft.  wide,  with  an  iron  fence  the  sections  of  which  shall  be  of 
equal  length ;  what  ie  the  length  of  the  longest  sections  that 
can  be  used  ? 

93.  What  number  multiplied  by  \  of  itself  equals  32  ? 

94.  What  number  multiplied  by  f  of  itself  equals  54  ? 

95.  What  number  is  that  which  if  doubled  and  the  product 
divided  by  3,  the  quotient  squared,  that  square  increased  by  \ 
of  itself,  the  result  will  be  \  of  the  square  of  12  ? 

96.  What  is  the  quotient,  if  the  cube  of  75  is  divided  by  \  of 
1000? 

97.  What  is  the  profit  of  buying  peaches  at  60  cents  a 
hundred,  if  10%  of  them  decay,  and  the  remainder  sell  at  2 
cents  apiece  ? 

98.  At  40  cents  per  centar,  what  would  it  cost  to  plaster  a 
hall  76  ft.  long,  54  ft.  wide,  and  18  ft.  high,  deducting  10%  for 
windows  and  woodwork  ? 


Test  Questions  for  Review.  285 

99.  How  many  bushels  of  wheat  equal  63  hektoliters? 

100.  What  is  75$  of  the  difference  between  the  square  root 
of  256  and  the  second  power  of  the  same  number  ? 

101.  A  field  containing  6  A.  12  sq.  r.  is  3  times  as  long  as  it 
is  wide ;  what  are  its  length  and  breadth  ? 

102.  What  is  the  smallest  sum  of  money  for  which  you  can 
buy  oxen  at  $85,  or  cows  at  $35  each  ? 

103.  What  is  the  distance  from  a  comer  of  a  cubical  block 
to  the  opposite  diagonal  corner,  the  sides  being  9  sq.  feet  ? 

104.  A  field  \  as  wide  as  it  is  long  contains  8 J  A.  32  sq.  r.; 
what  length  of  fence  is  required  to  go  around  it  ? 

105.  A  man  paid  for  tobacco  an  average  of  $25  a  year  from  the 
age  of  18  until  he  was  60,  when  he  died  and  left  $1500  for  his 
heirs ;  if  he  had  deposited  in  the  savings  bank  each  year  the 
money  spent  for  tobacco,  how  much  might  he  have  left  at  b% 
semi-annual  compound  interest? 

106.  The  diameter  of  a  circle  is  10  inches  ;  what  is  the  side 
of  the  square  that  may  be  inscribed  in  it  ? 

Note. — The  diameter  of  a  circle  forms  the  hypothenuse  of  the  two 
right-angled  triangles  which  equal  the  square  inscribed  in  it. 

107.  What  is  the  side  of  a  square  equal  in  area  to  a  circle 
150  meters  in  diameter? 

108.  In  what  time  will  $1265  at  6%,  yield  $85.25  ? 

109.  If  the  interest  of  $3865  for  8  mo.  is  $180.03,  what  would 
be  the  principal  on  which  $360.85  is  paid  for  2  yr.  4  mo.  15  days? 

no.  Find  the  difference  between  the  square  root  of  the  least 
common  multiple  of  6,  12,  18,  36,  48,  and  the  square  of  their 
greatest  common  divisor. 

in.  In  15  hektars  how  many  square  rods? 

112.  An  agent  sold  flour  at  $7.92  a  barrel,  at  a  loss  of  4%;  at 
what  price  should  it  be  sold  to  gain  8%  ? 

113.  In  126589  meters  how  many  kilometers  ? 

114.  How  many  miles,  rods,  etc.,  in  the  above? 

115.  If  flour  sold  at  $12  a  barrel  gains  15$,  what  would  be 
the  gain  %  if  sold  at  $11.25  ? 


m 


If 

* s>   j   (  _ 

PPENDIX. 

(1     g ^15r^ a     «* 

DRILL     EXERCISES. 


691.  The  following  and  similar  exercises  should  be  practised 
till  the  combinations  can  be  read  without  hesitation  : 


(1.) 

(2- 

) 

(3.) 

M 

(5.) 

6. 

59  75 

643 

74 

725  87 

8462  34 

7425  34, 

a. 

7. 

27  82 

350 

62 

842  73 

2351  23 

6534  23, 

b. 

8. 

46  71 

128 

49 

523  27 

3162  34 

5623  14, 

c. 

9. 

28  15 

352 

73 

435  54 

4273  43 

4731  25, 

d. 

10. 

34  63 

243 

25 

327  43 

5384  52 

5842  36, 

e. 

11. 

29  50 

455 

63 

276  32 

6275  63 

4953  27, 

f. 

12. 

68  71 

729 

31 

586  34 

3284  32 

2586  54, 

&• 

13. 

97  53 

426 

76 

235  20 

1635  34 

4234  62, 

h. 

14. 

82  43 

623 

25 

463  52 

2586  89 

1736  44, 

i. 

15. 

64  25 

321 

35 

958  76 

7434  26 

5398  29, 

J- 

16. 

18  12 

238 

17 

386  29 

5869  73 

1234  56, 

k. 

17. 

19  50 

125 

51 

315  46 

3276  42 

7891  01, 

1. 

18. 

62  25 

436 

25 

434  57 

1635  38 

1234  16, 

m. 

19. 

64  37 

536 

63 

372  46 

5913  84 

6843  75, 

n. 

20. 

53  63 

257  47 

657  32 

6284  35 

7616  24, 

0. 

P. 


a. 


R. 


s. 


Note. — The  numbers  in  the  above  examples  should  be  added  perpen. 
dicularly  for  the  first  five  examples,  then  horizontally  through  the  20th. 
They  may  be  taken  in  columns  of  two  or  more  figures  at  a  time. 

Subteaction. — 21,  22.  In  col.  marked  "P"  (at  bottom) 
subtract  7th  from  6th  ;  9th  from  8th. 

23-28.  In  "  T  *  take  b  from  a ;  d  from  c ;  f  from  e ;  g  from 
h ;  i  from  j  ;  k  from  1. 


Drill  Exercises,  287 

29-34.  In  "S"  take  b  from  a;  c  from  d;  e  from  f;  h  from 
g ;  i  from  j  ;  1  from  k. 

Multiplication. — 35-50.  Multiply  the  numbers  in  "  T  "  by 
those  in  "P,"  begin  "a." 

Division". — 51-65.  Divide  each  of  the  above  products  by  the 
numbers  in  i  ■  Q." 

Note. — These  exercises  may  be  continued  and  extended  at  pleasure. 

Drill    in     Percentage. 

692.    l.  Selling  price  $95,  cost  $84  ;  required  the  gain  %. 

2.  Profit  $30,  cost  $128.50  ;  required  the  gain  %. 

3.  Loss  12%,  cost  $125.25  ;  required  selling  price. 

4.  Selling  price  $225.50,  loss  18%  ;  required  cost. 

5.  Cost  $120,  selling  price  $160  ;  required  gain  %* 

6.  Profit  $350,  cost  $800  ;  required  gain  %. 

7.  Loss  $25.50,  cost  $175  ;  required  loss  %. 

8.  Selling  price  $1875,  loss  15% ;  required  cost. 

9.  Profit  6£%,  cost  $1200  ;  required  selling  price. 

10.  Principal  $240,  int.  $26.40,  rate  8\%\  required  time. 

11.  Principal  $450.75,  rate  9%,  time  4  yr.  7  mo.  15  d.;  amount? 

12.  Principal  $425.45,  rate  6%,  time  3  yr.  6  mo. ;  required 
compound  interest. 

13.  Insured    $6700,   rate    \%,    time    1   yr.;    required    the 
premium. 

14.  Principal  $800,  interest  $32,  time  8  mo.;  required  rate. 

15.  Tax  $12500,  property  $2400000;  required  rate. 

16.  Principal  $2500,  time  1  yr.  4  mo.,  rate  7-&%;  amount? 

17.  Difference  discount  and  int.  of  $900,  3  yr.  4  mo.  20  d.-  6$. 

18.  Bank  discount  $168.13,  at  6%  ;  8  yr.  5  mo. 

19.  Bank  discount  $900,  at  8% ;  9  months.. 

20.  Amount  £35  4s.  6d.,  2  yr.  8  mo.,  at  6$; 

21.  Net  proceeds  320  A.,  at  $22.50;  commission  lQ%. 

22.  Insurance  $10000,  at  \%  ;  policy  $1. 


288  Appendix. 

23.  Cost  $400  for  9  cwt.  52  lb.  coffee,  gain  1%%  ;  required 
selling  price. 

24.  Interest  $685.50,  at  10%,  time  3  yr. ;  required  principal. 

25.  Paid  $6180,  brokerage  3%  ;  required  amt.  of  draft. 

26.  Discount  $1600  for  60  d.,  6%;  required  the  avails. 

27.  Amt.  $860  from  Jan.  25,  1882  to  Jan.  5,  1883,  at  9%. 

28.  Amount  of  $124.17  for  11  mo.  29  d.,  at  9%. 

29.  Interest  of  $3000  for  6  mo.  15  d.,  at  7&%. 

30.  Prin.  $860.56,  int.  $149.63,  time  2  yr.  8  mo.  3  d. ;  rate  ? 

31.  Avails  of  note,  $8000,  at  6%,  6  mo.;  required  its  face. 

32.  Principal  $475,  at  6%,  amount  $57095  ;  rate. 

33.  Present  worth  of  $2500,  due  in  9  mo.,  6%. 

34.  Cost  of  bill  $2500,  discount  %\%  ',  required  the  face. 

35.  Principal  $750,  amount  $960.85  at  7^%  ;  time. 

36.  Gain  $384,  at  12-|%  J  required  the  cost. 

37.  Interest  of  $1200  for  2  yr.  3  mo.  $168.75  ;  required 
the  rate. 

38.  Prin.  $5000,  at  7T3o%,  from  Jan.  1  to  March  1,  1884 ; 
required  the  accurate  interest. 

39.  Income  is  $800  from  IT.  S.  5's,  at  104  ;  required  the 
investment. 

40.  Prin.  $860,  at  6%,  amount  $900  from  Jan.  1  to  what  day? 

41.  Bought  bill  of  goods  amounting  to  $6845,  and  less  charges 
$65,  sold  same  at  12-§-%  advance,  took  note  for  60  d.  and  with 
proceeds  from  6%  discount,  bought  bill  on  London  at  109J  ; 
required  the  face  of  the  bill. 

42.  Goods  marked  25%  advance  on  cost,  are  sold  at  15% 
below  the  marked  price  ;  what  per  cent  is  the  gain  ? 

43.  If  you  hire  money  at  a  bank,  at  6%  for  4  mo.,  to  buy  a 
horse  at  $180,  what  does  the  horse  really  cost  you  ? 

44.  What  rate  of  interest  does  a  man  pay,  who  gets  his  notes 
discounted  at  a  bank  for  90  days  at  6%  ? 

45.  If  a  bank  borrows  $100000  at  6  per  cent  and  discounts  a 
30-day  paper  for  the  same  amount  at  6  per  cent,  what  are  the 
profits  ? 


Drill  Exercises.  289 

46.  The  true  discount  of  81215,  due  in  10  mo.  20  d.,  is  890 ; 
what  is  the  rate  ? 

47.  Which  is  better,  and  how  much,  6%  bonds  at  90,  or  8% 
bonds  at  130,  both  due  at  the  same  time  ? 

Metric    Drill. 

693.  l.  A  man  sold  J  of  a  farm  of  170  hektars,  which  cost 
500055  francs,  at  3500  fr.  per  Ha.,  T^  of  it  at  2800  fr.  per  Ha,, 
and  the  remainder  at  cost;  what  was  the  gain  or  loss? 

2.  If  with  34  kilograms  of  wool,  25  meters  of  flannel  60 
centims  wide  can  be  made,  what  length  of  similar  flannel,  80 
centims  wide,  can  be  made  with  108  Kg.  of  wTool  ? 

3.  How  many  fields  containing  2  Ha.  47  ars  each  can  be 
made  on  a  farm  of  313  Ha,  and  69  ars? 

4.  How  many  hektoliters  of  wheat  will  a  bin  contain  which 
is  7  meters  square  and  2.7  meters  deep  ?  What  will  it  cost  at 
$2  per  bushel  ? 

5.  Express  the  rate  per  hour  of  a  mail  train  in  terms  of  that 
of  a  mail  cart,  the  former  traveling  4J  myriameters  an  hour, 
the  latter  135  kilometers  in  10  hours  ? 

6.  If  26  men  working  10  hr.  a  day  can  dig  a  trench  50  meters 
long,  4  meters  25  centims  broad,  and  6£  meters  deep  in  12  d., 
how  many  men  will  it  require  to  dig  a  similar  trench  125 
meters  long,  3  meters  6  cm.  broad,  and  9  m.  35  cm.  deep  in  18 
d.,  if  they  work  12  hr.  a  day? 

7.  It  requires  14375  sq.  bricks  to  pave  a  path  184  meters 
long  and  4  m.  5  centims  broad ;  find  the  side  of  each  brick. 

8.  What  is  the  radius  of  a  circular  bed  whose  circumference 
is  3  meters  50  centimeters  ? 

9.  If  13  square  meters  20  square  decims  of  canvas  are 
required  to  cover  a  cylindrical  column,  the  radius  of  whose 
base  is  28  centims ;  what  is  the  height  of  the  column  ? 

10.  If  a  pipe  3  centims  in  diameter  will  empty  a  cistern  in  8 
min.,  what  is  the  diameter  of  a  pipe  that  will  empty  it  in  18  min.? 

li.  How  many  cubic  decimeters  in  a  globe  6  decimeters  in 
diameter  ? 


290  Appendix. 


GREATEST     COMMON     DIVISOR    OF     FRAC- 
TIONS. 

694.  The  Greatest  Common  Divisor  of  two  or  more  fractions 
is  the  greatest  number  that  will  divide  each  of  them  and  give 
an  integer  for  the  quotient. 

695.  To  find  the  Greatest  Common  Divisor  of  two  or  more 
fractions. 

I.  Find  the  g.  c.  d.  of  -f,  if,  and  2f . 

Analysis.— Reducing  if  to  lowest  terms,  2f  operation. 

to  an  improper  fraction,  and  all   to   the  least  ^-|  —  -f^,    2-f-  =  -%0-. 

common  denominator  ;  the  fractions  are  |f,  f f,  led               =  45. 

and  Y/.     The  <j,  c.  d.  of  the  numerators  is  4.  7     -P  "NT  -       4. 

Since  36,   24,  and  100  denote  45ths,  it  follows  Q\  C'  tl*  0t  SSm  ~ 

that  their  g,  c.  d.  is  not  4  integral  units,  but  4  Hence,  ^j,   Ans. 
forty- fifths  of  1  unit.     Hence,  the 

Eule. — I.  Reduce  mixed  numbers  to  improper  frac- 
tions, compound  and  complex  fractions  to  simple  ones, 
and  all  to  lowest  terms. 

II.  Reduce  these  fractions  to  the  least  common  denom- 
inator, and  write  the  greatest  common  divisor  of  the 
numerators  over  it. 

Find  the  fj.  c.  d.  of  the  following  fractions : 


2-  A,  1  f 

5.  12f,  8J,  9J.. 

8.  *,  ItV.  la- 

3.  }  of  f,  1\,  4|. 

6-   i,  f,  h  f 

s'-  ii  i,  n- 

4.  i,  i,  i,  !• 

7.   3A,  M,  Ht- 

10.  |^ff,  8f 

11.  A  farmer  has  67|  bu.  oats,  33|  bu.  rye,  and  70-J  btt. 
wheat,  which  he  wishes  to  keep  separate  and  send  to  market 
in  the  largest  bags  possible,  each  containing  the  same  number 
of  bushels;  required  the  number  of  bags,  and  the  quantity 
in  each. 


Least  Common  Multiple  of  Fractions.        291 

12.  A  man  has  4  fields  containing-  6$  A.,  7T^-0-  A.,  10|  A., 
and  8|  A.  respectively,  which  he  divided  into  the  largest 
possible  house  lots  of  equal  size ;  how  many  lots  did  he  make, 
and  what  was  the  size  of  each  ? 

LEAST     COMMON     MULTIPLE      OF      FRAC- 
TIONS. 

696.  The  Least  Common  Multiple  of  two  or  more  fractions 
is  the  least  number  that  can  be  divided  by  each  of  them  and 
give  an  integer  for  the  quotient. 

697.  To  find  the  I,  c.  m.  of  two  or  more  fractions. 

I.  What  is  the  I.  C  m.  off,  ^,  and  2^-? 

Analysis. — Reducing  T\  to  lowest  terms,  operation. 

and  2fV  to  an  improper  fraction,  the  given  ^  —  J y    2^  =  ^-J. 

fractions  become  f,  £,  and  ff,  and  the/,  r.m.       j    (t    „,}i    of  N    33 

of  the  numerators  is  33.     Since  the  numera-  i      £  t\ 

tors  3,   3,  and   33   are   dividends,    and  the      9*  <'"  <*•  oi  ■L)-  =     4- 

denominators  8,  4,  and  16  are   divisors,  it       Hence,  ^3-  =  8J.  AflS. 

follows  that  the  I.  c,  tn.  33,  is  not  33  integral 

units,  but  so  many  fractional  parts  of  the  greatest  common  divisor  of  the^- 

denominators,  which   is  4.     And   4  placed  under  33  forms  the  fraction 

^  =  8£,  which  is  the  /.  c.  m.  required.     Hence,  the 

Eule. — I.  Reduce  mixed  numbers  to  improper  frac- 
tions, compound  and  complex  fractions  to  simple  ones, 
and  all  to  their  lowest  terms. 

II.  Find  the  least  common  multiple  of  the  numera- 
tors and  write  it  over  the  Greatest  common  divisor  of  the 
denon  vinators. 

Mud  the  I.  c.  m.  of  the  following  fractions : 
3.     5i,7J,3flf,  5.     16^,8^,  5tV 


292 


Append* 


IX. 


6.  A,  B,  and  C  start  at  the  same  time  and  place  to  go  round 
a  circular  race-course;  A  can  make  the  circuit  in  |  of  a  day, 
B  in  f,  and  C  in  £  of  a  day  ;  in  how  many  days  will  they  first 
meet  at  the  place  of  starting,  and  how  many  times  will  each 
have  gone  round  the  course  ? 

7.  Three  yachts  start  at  the  same  time  and  place  to  sail 
round  a  light-boat,  1  mile  distant;  the  first  sails  52  r.  a  min- 
ute, the  second  70  rods,  and  the  third  100  rods  a  minute  ;  when 
will  they  first  be  together,  and  how  far  from  the  starting  point? 

8.  In  a  certain  park,  the  circular  walk  is  one  mile  long. 
Three  boys  undertook  to  walk  around  this  in  one  direction  till 
all  should  meet  again  at  the  starting  point;  No.  1,  walks  2}  m. 
an  hour;  No.  2,  3J  m.;  No.  3,  A\  m.;  how  many  hours  must 
they  walk,  and  how  many  times  must  each  go  around? 


Table  of   Prime   Numbers   from    I   to  3407. 


1 

173 

409 

659 

941 

1223 

1511 

1811 

2129 

2423 

2741 

3079 

2 

179 

419 

661 

947 

1229 

1523 

1823 

2131 

2437 

2749 

3083 

3 

181 

421 

673 

953 

1231 

1531 

1831 

2137 

2441 

2753 

3089 

5 

191 

431 

677 

967 

1237 

1543 

1847 

2141 

2447 

2767 

3109 

7 

193 

133 

683 

971 

1249 

1549 

1861 

2143 

2459 

2777 

3119 

11 

197 

439 

691 

977 

1259 

1553 

1867 

2153 

2467 

2789 

3121 

13 

199 

443 

701 

983 

1277 

1559 

1871 

2161 

2473 

2791 

3137 

17 

211 

449 

709 

991 

1279 

1567 

1873 

2179 

2477 

2797 

3163 

19 

223 

457 

719 

997 

1283 

1571 

1877 

2208 

2503 

2801 

3167 

•  23 

227 

461 

727 

1009 

1289 

1579 

1879 

2207 

2521 

2803 

3169 

^  29 

229 

463 

733 

1013 

1291 

1583 

1889 

2213 

2531 

2819 

3181 

31 

233 

467 

739 

1019 

1297 

1597 

1901 

2221 

2539 

2833 

3187 

.  37- 

239 

479 

743 

1021 

1301 

1601 

1907 

2237 

2543 

2837 

3191 

*  41 

241 

487 

751 

1031 

1303 

1607 

1913 

2239 

2549 

2843 

3203 

43 

251 

491 

757 

1033 

1307 

1609 

1931 

2243 

2551 

2851 

3209 

47 

257 

499 

761 

1039 

1319 

1613 

1933 

2251 

2557 

2857 

3217 

53 

263 

503 

769 

1049 

1321 

1619 

1949 

2267 

2579 

2861 

3221 

59 

269 

509 

773 

1051 

1327 

1621 

1951 

2269 

2591 

2879 

3229 

61 

271 

521 

787 

1081 

1361 

1627 

1973 

2273 

2593 

2887 

3251 

67 

277 

523 

797 

1063 

1367 

1637 

1979 

2281 

2609 

2897 

3253 

71 

281 

541 

809 

1069 

1373 

1(557 

1987 

2287 

2617 

2903 

3257 

73 

2S3 

547 

811 

1087 

1381 

1663 

1993 

2293 

2621 

2909 

3259 

79 

298 

557 

821 

1091 

1399 

1667 

1997 

2297 

2633 

2917 

3271 

83 

307 

563 

823 

1093 

1409 

1069 

1999 

2309 

2647 

2927 

3299 

89 

311 

569 

827 

1097 

1438 

1693 

2003 

2311 

265? 

2939 

&301 

97 

313 

571 

829 

1103 

1427 

1697 

2011 

2333 

2659 

2953 

3307 

101 

317 

577 

839 

1109 

1429 

1699 

2017 

2339 

2663 

2957 

3313 

103 

331 

587 

853 

1117 

1433 

1709 

2027 

2341 

2671 

2963 

3319 

107 

337 

593 

857 

1123 

1439 

1721 

2029 

2347 

2677 

2969 

3323 

109 

347 

599 

859 

1129 

1447 

1723 

2039 

2351 

2683 

2971 

3329 

113 

349 

601 

863 

1151 

1451 

1733 

2053 

2357 

2687 

2999 

3331 

127 

353 

607 

877 

1153 

1453 

1741 

2063 

2371 

2689 

3001 

3343 

131 

359 

613 

881 

1163 

1459 

1747 

2069 

2377 

2693 

3011 

3347 

137 

367 

617 

883 

1171 

1471 

1753 

2081 

2381 

2699 

3019 

3359 

139 

373 

019 

887 

1181 

1481 

1759 

2083 

23*3 

2707 

3023 

3861 

149 

379 

631 

907 

1187 

1483 

1777 

2087 

2389 

2711 

3037 

3371 

151 

383 

641 

911 

1193 

1487 

1783 

2089 

2393 

2713 

3041 

3373 

157 

389 

643 

919 

1201 

1489 

1787 

2099 

2399 

2719 

3049 

3389 

163 

397 

047 

929 

1213 

1493 

1789 

2111 

2411 

2729 

3061 

3391 

16? 

491 

653 

937 

1217 

1499 

1801 

2113 

2417 

2731 

3067 

3407 

Contractions  in  Multiplication.  293 

698.  Property  of  the  number  9 : 

Any  number  divided  by  9  will  leave  the  same  remainder  as 
the  sum  of  its  digits  divided  by  9. 

1.  Let  it  be  required  to  find  the  excess  of  9's  in  7548467. 

Adding  7  to  5,  the  sum  is  12.  Rejecting  9  from  12,  leaves  3 ;  3  and 
4  are  7,  and  8  are  15.  Rejecting  9  from  15,  leaves  6 ;  6  and  4  are  10. 
Rejecting  9  from  10,  leaves  1  ;  1  and  6  are  7,  and  7  are  14.  Finally, 
rejecting  9  from  14  leaves  5,  the  excess  required. 

Note. — It  will  be  observed  that  the  excess  of  9's  in  any  two  digits 
is  always  equal  to  the  sum,  or  the  excess  in  the  sum,  of  those  digits. 
Thus,  in  15  the  excess  is  6,  and  1  +  5=6;  so  in  51  it  is  6,  and  5  +  1  =  6. 

699.  To  prove  Multiplication  by  Excess  of  9's. 

Find  the-  excess  of  9 's  in  each  factor  separately;  then 
multiply  these  excesses  together,  and  reject  the  9's  from 
the  result ;  if  this  excess  agrees  with  the  excess  of  9's  in 
the  answer,  the  work  is  right.  <«  • 

2.  What  is  the  product  of  1842  x  324  ? 

1842     Excess  of  9's  in  the  multiplicand  is  6. 
324    Excess  of  9's  in  the  multiplier  is  0. 

596808,  Ans.9  6x0  =  0.    The  excess  of  9's  in  prod,  is  also  0. 

3.  Multiply  54683  by  348  and  prove  the  answer. 

CONTRACTIONS     IN    MULTIPLICATION.     ' 

700.  To  multiply  by  any  number  within  12  (or  less)  of  100, 
1000,  etc. 

Eule. — Annex  as  many  ciphers  to  the  multiplicand  as 
there  are  figures  in  the  multiplier, and  subtract  as  many 
times  the  multiplicand  from  the  result  as  there  are 
units  in  the  complement  of  the  multiplier. 

1.  Multiply  2564  by  993. 

Solution.— 1000-993  =  7  ;  2564 x7  =  17948. 
2564000-17948  =  2546052,  Arts. 

2.  Multiply  5863  by  88.  4.  Multiply  54326  by  991. 

3.  Multiply  45832  by  989.  5.   Multiply  67543  by  9996. 


294  Appendix. 

701.  To  square  any  number  between  50  and  60. 

Rule. — Add  the  units  of  the  given  number  to  25  for 
the  hundreds,  and  for  the  tens  and  units  annex  the 
square  of  the  units. 

6.  Find  the  square  of  53. 

Solution.— 52  =  25,  and  25  +  3  (the  units)  =  28  ;  32  =  9 ;  2809,  Ans. 

7.  What  is  the  square  of  54?     Of  55  ?     Of  58  ? 

8.  What  is  the  square  of  52  ?     Of  56  ?     Of  59  ? 

702.  To  square  a  number  ending  in  5. 

Rule. — Multiply  the  number  of  tens  by  itself  plus  1, 
and  to  the  right  of  the  product  annex  25. 

9.  What  is  the  square  of  25  ? 

Solution.— The  tens  (2)  plus  1  =  3,  and  2x3  =  6,  then  625,  Arts. 

10.  What  is  the  square  of  45  ?     Of  G5  ?     Of  85  ?     Of  95  ? 
Note. — This  rule  may  be  extended  to  more  than  two  places  of  figures. 

11.  Find  the  square  of  125. 

Solution. — 12  x  13  =  156  and  25  annexed  =  15625,  Ans. 

12.  Find  the  square  of  105.     Of  115.     Of  145.     Of  135. 

703.  To  multiply  any  number  by  II. 

Rule. — On  the  right  place  the  units  of  the  multipli- 
cand, then  add  the  digits  successively  from  right  to  left, 
carrying  as  usual,  and  write  results  in  the  product. 

13.  Multiply  4572  by  11.  , 

Solution. — Place  2  for  the  first  product  figure,  then  2  +  7  =  9  (the  2d), 
7  +  5  =  12  (2  the  3d),  5  +  4  +  1  =  10  (0  the  4th),  and  4  +  1  (carried)  =  5,  the 
last  figure.     Then  50292,  Ans. 

14.  Multiply  5364  by  11.  16.   2693  x  11  =  ? 

15.  Multiply  7532  by  11.  17.  2854  x  11  =  ? 


Finding  the  Time  between  Two  Dates.       295 

704.  The  product  of  the  sum  and  difference  of  two  numbers 
is  equal  to  the  difference  of  their  squares. 

705.  The  square  of  any  number  consisting  of  tens  and  units 
is  equal  to  the  square  of  the  tens,  plus  tiuice  the  product  of  the 
tens  by  the  units,  plus  the  square  of  the  units. 

706.  The  cube  of  any  number  consisting  of  tens  and  units  is 
equal  to  the  cube  of  the  tens,  plus  3  times  the  square  of  the  tens 
by  the  units,  plus  S  times  the  tens  by  the  square  of  the  units, 
])lux  the  cube  of  units. 


Finding    the    Time    between     Two     Dates. 

707.  The  process  of  finding  the  time  between  two  dates  by 
Compound  Subtraction  is  liable  to  lead  to  error  in  consequence 
of  the  greater  number  of  days  in  some  months  than  in  others. 

It  is  the  custom  with  Banks  when  the  time  is  given  in 
months,  to  consider  them  calendar  months  in  reference  to  the 
maturity  of  the  paper,  but  even  then  they  compute  the 
discount  by  days. 

Time  table,  showing  the  number  of  days  : 


To  the  Corresponding  Day 

OP 

From  any 
Day  of 

1 

2 

3 

4 

.5 

6 

7         8 

9 

10 

11 

12 

Jan. 

Feb. 

Mar 

Apr. 

May 

June. 
151 

July. 

Aug. 

Sept. 

Oct. 
273 

Nov. 
304 

Dec. 
334 

January  . . . 

BBS 

31 

59 

90 

120 

181 

212 

243 

February  . . 

334 

365 

23 

59 

89 

120 

150       181 

212 

242 

273 

303 

March 

30(5 

337 

365 

31 

61 

92 

122 

153 

184 

214 

245 

275 

April 

275 

306 

334 

365 

30 

61 

91 

122 

153 

183 

214 

244 

May 

245 

276 

304 

335 

365 

31 

61 

92 

123 

153 

184 

214 

June  

214 

245 

273 

304 

834 

365 

30 

61 

92 

122 

153 

183 

July 

184 

215 

243 

274 

304 

335 

365 

31 

62 

92 

123 

153 

August    . . . 

153 

184 

212 

243 

273 

304 

334 

365 

31 

61 

92 

122 

September. 

122 

153 

181 

21-2 

242 

273 

303 

334 

365 

?0 

61 

91 

October 

92 

123 

151 

182 

212 

243 

273 

304 

335 

365 

31 

61 

November  . 

Gl 

93 

120 

151 

181 

21-> 

242 

273 

304 

334 

365 

30 

December. . 

31 

62 

M 

121 

151 

182 

212 

243 

274 

304 

335 

365 

l.   How  many  days  from  May  13  to  Aug.  23  ? 

Explanation.— Find  "May"  in  the  column  of  months  at  the  left; 
and  on  the  same  line  under  "  Aug."  find  92,  which  is  the  number  of  days 
from  any  day  in  May  to  the  same  dr-f  in  Aug.  But  Aug.  23  is  10  days 
more  than  Aug.  13,  and  92  +  10  =  102  d.,  Ana. 


296  Appendix. 

Note.— If  the  required  date  be  earlier  in  the  month  than  the  date  from 
which  the  time  is  counted,  subtract  the  difference  from  the  tabular  number. 

2.  How  many  days  from  May  13  to  Aug.  1  ? 

Explanation.— From  May  to  Aug.  is  92  d.,  but  to  Aug.  1  is  12  d. 
less  than  to  Aug.  13  ;  and  92—12  =  80  d.,  Ans. 

Note. — If  the  given  date  is  in  a  leap  year  it  will  be  necessary  to  add 
cr  subtract  one  more  day  when  Feb.  intervenes 

708.  If  it  is  required  to  find  a  day  which  is  a  given  number 
of  days  after  a  certain  date,  look  in  the  table  opposite  the  mo. 
having  the  given  date,  and  find  the  number  of  days  next  larger, 
subtract  the  given  days  and  count  back  for  the  required  date. 

3.  Find  the  date  that  is  125  days  after  July  4th. 

Explanation.— Opposite  July,  the  next  larger  number  than  125,  is 
153  in  Dec;  153-125  =  28,  and  31-28  =  3.     Hence,  Nov.  G  is  tha  date. 

709.  To  find  the  time  for  which  a  note  must  be  drawn,  so  that 
it  will  not  fall  due  on  Sunday  or  a  Legal  Holiday. 

Rule. — Find  the  number  of  days  by  the  Table,  and 
dividing  them  by  7,  the  quotient  will  be  the  number 
of  weeks  and  days.  Then  count  the  odd  days  from  the 
day  of  the  week  on  which  the  note  is  dated. 

4.  A  note  was  drawn  on  Friday  the  1st  of  Feb.,  to  run  3 
months ;  what  day  of  the  week  will  it  fall  due  ? 

Solution. — Three  months  from  Feb.  1st  brings  May  1st,  which  by 
Table  is  89  d.  in  a  common  year,  or  90  d.  leap  year.  89-5-7  =  12  and  5  d. 
over.     Friday +  5  d.  gives  Wednesday,  or  in  leap  year,  Thursday. 

5.  If  a  note  is  dated  Tuesday,  Apr.  1st,  to  run  60  days,  what 
day  of  the  week  will  it  fall  due  ? 

6.  The  birthday  of  Shakspeare  was  April  23,  1564;  how 
many  years,  months,  and  days  from  that  to  the  present  time  ? 

7.  Suppose  a  note  is  made  on  Wednesday,  the  13th  of  Feb., 
1884,  payable  in  3  months  from  date;  what  day  would  it  be 
due? 


Life  Insurance  Tables. 


297 


LIFE     INSURANCE     TABLES. 

710.  The  Expectation  of  Life  is  the  probable  number  of 
years  a  person  may  live  after  he  has  reached  a  specified  age. 
It  is  found  by  dividing  the  number  of  those  who  survive 
that  age  by  the  number  of  those  who  attain  it. 

American     Experience    Table    of     Mortality. 

Adopted  by  the  State  of  N.  Y.  in  estimating  life  endowments. 


Com- 

Number 

Deaths 

Com- 

Number 

Deaths 

Com- 

Number 

Deaths 

pleted 

surviving  at 

in  each 

pleted 

surviving  at 

in  each 

pleted 

surviving  at 

in  each 

Age. 

each  Age. 

Year. 

Age. 

each  Age. 

Year. 

Age. 

each  Age. 

Year. 

10 

100.000 

749 

40 

78,106 

765 

70 

38,569 

2,391 

11 

99,251 

745 

41 

77,341 

774 

71 

36,178 

2,448 

12 

98,505 

743 

42 

76,567 

785 

72 

33,730 

2,487 

13 

97,762 

740 

43 

75,782 

797 

73 

31,243 

2,505 

14 

97,022 

737 

44 

74,985 

812 

74 

28,738 

2,501 

15 

96,285 

735 

45 

74,173 

828 

75 

26,237 

2,476 

16 

95,550 

732 

46 

73,345 

848 

76 

23,761 

2,431 

17 

'  94,818 

729 

47 

72,497 

870 

77 

21,330 

2,369 

18 

94,089 

727 

48 

71,627 

896 

78 

18.961 

2,291 

19 

93,362 

725    | 

49 

70,731 

927 

79 

16,670 

2,196 

20 

92,637 

723 

50 

69,804 

962 

80 

14,474 

2.091 

21 

91,914 

722 

51 

68,842 

1001 

81 

12,383 

1,964 

22 

91,192 

721 

52 

67,841 

1,044 

82 

10,419 

1,816 

23 

90,471 

720 

53 

66,797 

1,091 

83 

8,608 

1,648 

24 

89,751 

719 

54 

65,706 

1,143 

84 

6,955 

1,470 

25 

89,032 

718 

55 

64,563 

1,199 

85 

5,485 

1,202 

26 

88,314 

718 

56 

63,364 

1,260 

86 

4,193 

1,114 

27 

87,596 

718 

57 

62,104 

1,325 

87 

3,079 

933 

28 

86,878 

718 

58 

60,779 

1,394 

88 

2,146 

744 

29 

86,160 

719 

59 

59,385 

1,468 

89 

1,402 

555 

30 

85,441 

720 

60 

57,917 

1,546 

90 

847 

385 

31 

84,721 

721 

61 

56,371 

1,628 

91 

462 

246 

32 

84,000 

723    i 

62 

54,743 

1,713 

92 

216 

137 

33 

83,277 

726 

63 

53,030 

1,800 

93 

79 

58 

34 

82,551 

729    ; 

64 

51,230 

1,889 

94 

21 

18 

35 

81,822 

732    : 

65 

49,341 

1,980 

95 

3 

3 

36 

81090 

737 

66 

47,361 

2,070 

37 

80,353 

742 

67 

45,291 

2,158 

38 

79,611 

749 

68 

43,1&3 

2,243 

39 

78,862 

756 

69 

40,890 

2,321 

Notes. — 1.    Wigglesicorth's  tables,  prepared  from  data  in  this  country, 
have  been  adopted  by  Massachusetts  in  estimating  life  estates. 


298  Appendix. 

2.  Among  the  prominent  English  tables  of  mortality  are  the  Carlisle 
tables  by  Milne,  and  the  Northampton  tables  by  Dr.  Price.  The  former 
are  generally  used  in  England. 

711.  According  to  the  Carlisle  tables,  of  10000  persons  born 
together,  5528  reach  32,  and  2771  reach  G7  years  of  age.  The 
expectation  of  life  to  the  age  of  67  therefore,  of  a  person  now 
32  is  §||-|-  =  \  nearly,  or  1  chance  in  2. 

Illustration. — What  is  the  net  premium  to  insure  $1  during  the 
year  succeeding  the  age  of  60,  the  present  age  being  40  ? 

By  Table,  the  number  living  at  60  is,     ...     .      57917 

61  is,     ...     .      56371 

The  number  dying  during  the  year  is,  .        1546 

Pres.  w.  of  $1,  due  in  20  y.  at  4=%  (Art.  306,  N.  3),  .  $.45638 

Present  worth  of  $1546  =  $705,563 

By  Table,  the  number  surviving  at  40  is  78106. 
Then,  705.563-^-78106  =  .00903,  net  premium. 

Explanation. — The  Table  above  shows  that  of  78106  persons  now 
living  at  the  age  of  40,  1546  will  die  during  the  year  succeeding  60.  The 
present  worth  at  4  %  of  $1546  payable  20  years  hence  is  $705,563,  which 
divided  among  78106  persons  now  living,  gives  the  premium  which  would 
secure  an  insurance  of  $1  to  each  of  them  in  case  of  death  during  the 
given  year. 


LIFE    ESTATES    AND    ANNUITIES. 

712.  The  rule  prescribed  in  New  York  State  for  estimating 
the  value  of  life  estates  is  as  follows : 

84th  Rule  of  the   Supreme  Court  to  ascertain  the  gross  sum 
in  payment  of  life  estates. 

Whenever  a  party,  as  a  tenant  for  life,  or  by  the  courtesy,  or  in  dower, 
is  entitled  to  the  annual  interest  or  income  of  any  sum  paid  into  court, 
and  invested  in  permanent  securities,  such  party  shall  be  charged  with 
the  expense  of  investing  such  sum,  and  of  receiving  and  paying  over  the 
interest  or  income  thereof  ;  but  if  such  party  is  willing  and  consents  to 
accept  a  gross  sum  in  lieu  of  such  annual  interest  or  income  for  life,  the 
same  shall  be  estimated  according  to  the  then  value  of  an  annuity  at  six 
per  cent  on  the  principal  sum,  during  the  probable  life  of  such  person 
according  to  the  Portsmouth,  or 


Life  Estates  and  Annuities. 


299 


Northampton     Annuity    Table. 
713.  Showing  the  value  of  an  annuity  of  $1  at  6%. 


Age. 

No.  of  years 
purchase 

the  Annuity 
is  worth. 

Age. 

No.  of  years 
purchase 

the  Annuity 
is  worth. 

Age. 

No.  of  years 
purchase 

the  Annuity 
is  worth. 

| 

!     Age. 

Xo.  of  years 
purchase 

the  Annuity 
is  worth. 

1 

10.107 

25 

12.063 

49 

9.563 

73 

4.781 

2 

11.724 

26 

11.992 

50 

9.417 

74 

4.565 

3 

12.348 

27 

11.917 

51 

9.273 

75 

4.354 

4 

12.769 

28 

11.841 

52 

9. 129 

76 

4.154 

5 

12.962 

29 

11.763 

53 

9.980 

77 

3.952 

6 

13.156 

30 

11.682 

54 

8.827 

78 

3.742 

7 

13.275 

31 

11.598 

55 

8.670 

79 

3.C14 

8 

13.337 

32 

11.512 

56 

8.509 

80 

3.281 

9 

13.335 

33 

11.423 

57 

8.343 

81 

3.156 

10 

13.285 

34 

11.331 

58 

8.173 

82 

2.926 

11 

13.212 

35 

11.236 

59 

7.999. 

83 

2.713 

12 

13.130 

36 

11.137 

60 

7.820 

84 

2.551 

13 

13.044 

37 

11.035 

61 

7.637 

85 

2.402 

14 

12.953 

38 

10.929 

62 

7.449 

86 

2.266 

15 

12.857 

39 

10.819 

63 

7.253 

87 

2.138 

16 

12.755 

40 

10.705 

64 

7.052 

88 

2.031 

17 

12.655 

41 

10.589 

65 

6.841 

89 

1.882 

18 

12.562 

42 

10.473 

66 

6.625 

90 

1.689 

19 

12.477 

43 

10.356 

67 

6.405 

91 

1.422 

20 

12.398 

44 

10.235 

68 

6.179 

92 

1.136 

21 

12.329 

45 

10.110 

69 

5.949 

93 

0.806 

22 

12.265 

46 

9.090 

70 

5.716 

94 

0.518 

23 

12.200 

47 

9.846 

71 

5.479 

24 

12.132 

48 

9.707    j 

72 

5.241 

Rule. — Calculate  the  interest  at  6%,  for  one  year,  upon 
the  sum  to  the  income  of  which  the  person  is  entitled. 
Multiply  this  int.  by  the  number  of  years  purchase  set 
opposite  the  person's  age  in  the  Table,  and  the  product  is 
the  gross  value  of  the  life  estate  of  such  person  in  said  sum. 

l.  If  a  widow  42  years  of  age  is  entitled  to  dower  in  real 
estate  worth  $10500,  what  is  the  gross  present  value  of  her 
right  of  dower  ? 


300  Appendix. 

Solution.— J  of  $10500  =  $3500;  int.  1  yr.  at  6%  =$210.00.  The 
number  of  years'  purchase  which  an  annuity  of  $1  is  worth  at  the  age  of 
42  is  10.473,  and  $210  x  10.473  =  $2199.33,  Ans. 

2.  If  a  man  60  years  of  age  is  tenant  by  the  courtesy  in  the 
whole  of  an  estate  of  $8000,  what  is  the  gross  value  of  his  life 
estate  at  present  ? 

Note. — If  the  annuities  are  payable  semi-annually,  one-fifth  of  the 
value  of  a  year's  purchase  should  be  added  to  those  values. 

3.  A  lady  whose  estate  was  valued  at  $500000  died,  leaving 
her  husband,  then  45  years  old,  a  life  interest  in  the  whole 
estate  ;  what  was  the  gross  value  of  his  interest  at  her  death  ? 

4.  A  man  left  an  estate  worth  $15000,  of  which  his  widow, 
aged  54,  was  to  receive  during  her  life  the  interest  on  J,  payable 
semi-annually ;  what  was  the  gross  value  of  her  portion  in  the 
premises. 

5.  A  gentleman  purchased  a  life  annuity  of  $1000,  belonging 
to  a  person  20  years  old;  what  should  it  have  cost  him? 


BUSINESS     INFORMATION     AND     FORMS.* 

R  ECEI  PTS. 

714.  A  Receipt  is  a  written  acknowledgment  that  a  debt 
is  paid. 

Note. — A  man  is  not  bound  by  laic  to  give  a  receipt ;  but  by  courtesy 
and  custom  they  are  always  given  when  desired. 

715.  A  full  receipt  states  the  amount  received,  the  date, 
place,  and  kind  of  payment,  by  whom  and  in  whose  behalf  the 
payment  was  made,  by  whom  and  in  whose  behalf  received, 
and  to  what  debt  or  purpose  it  is  to  be  applied. 

When  the  receipt  is  signed  by  the  person  to  whom  the  pay- 
ment was  due,  his  signature  is  enough.  But  when  the  business 
is  done  through  an  agent,  he  writes  his  principal's  name,  and 
his  own  name  below  it,  with  "per"  or  "by"  as  a  prefix  to 
signify  the  agency. 

*  For  forms  of  Bills,  Notes,  Drafts--,  etc.,  see  pp.  79,  118, 133-136. 


Business  Information  and  Forms.  301 

Notes. — 1.  Partial  payments  should  be  endorsed  on  the  note  or  bond, 
and  the  party  making  the  payment  should  also  take  a  receipt  for  it. 

8.  When  a  receipt  is  given  by  a  person  who  makes  his  mark  instead  of 
writing  his  name,  it  should  be  witnessed. 

Receipt  in   Full. 

S225T7/W.  Boston,  Jan.  31,  1884. 

Received  from  H  J.  Smith,  Two  Hundred  Twenty-five  ffy 
Dollars,  in  full  of  all  demands,  to  date. 

Osgood  &  Co., 

per  W.  Simmons. 

For  Payment  on  Account. 

Philadelphia,  Feb.  4,  1884. 
Received  from  Wm.  Rowland,  One  Hundred  Forty-five  fyy 
Dollars,  on  account. 

For  a  Note. 

New  York,  March  1,  1884. 
Received  from  Everett  Graw  &  Co.,  their  note  of  this 
date,  at  three  months,   in  our  favor,  for  Eighteen  Hundred 
Tiventy-seven  f-fo  Dollars,  which,  when  paid,  will  be  in  full 
for  account  rendered  to  28th  inst. 
$1827^° .  J-  C.  Byrnes  &  Co. 

Receipt  for  Interest. 

New  York,  Jan.  15,  1884. 
Received  of  Ginn,  Heath  &  Co.,  Two  Hundred  Forty -six 
Dollars,  in  full  for  six  months  interest  due  this  day  on  their 
Bond  to  me,  bearing  date  Oct.  18,  1882,  for  Eight  Thousand 
Two  Hundred  Dollars. 

$246.  L-  E.  Clark. 

Due  Bill  for  Goods. 

New  York,  Feb.  6,  1884. 
Due  to  Henry  Jones,  on  demand,  Twenty-five  -ffo  Dollars, 
to  be  paid  in  goods  from  my  store. 
T®Kjr~  K.  H.  Macy. 


302  Appendix. 


Order  for  Goods. 

Brooklyn,  May  1,  1884. 
Messrs.  Journeay  &  Burnham, 

Gentlemen :— Please  pay  to  John  Wood,  or  order,  Sixty- 
three  Dollars  in  goods  from  your  store,  and  charge  the  same  to 
our  account. 

Burtis  &  Co. 

Installment  Receipt. 


CD 
O 

CD 


$2000.  400  Shares. 

Brooklyn  (£.  E.  ft.  QTompanrj. 

Received,  Brooklyn,  Jan.  £9,  1S&4,  of  A.  J.  Pouch, 

Two  Thousand  (Xollai^s,  being  Tvjenty-fLve  (Dollars  per 
Share,  and  the  Ihird  Installment  on  Four  Hundred 
Shares  of  the  Capital  Stock  of  the  Brooklyn  Elevated 
Railroad  Company;  for  which  said  Shares  a  full 
Certificate  will  be  given,  upon  payment  of  all  Install- 
ments due  thereon,  and  the  surrender  of  this  Certificate. 

C D ,  A B , 

Secretary,  (president. 


Shipping    Receipt. 


Albany,  Jfay  9,  '84-. 

JHbany,Jtfay  9,  '84-  \      Received  from  Wm.  Wfills  $  Co.,  in 

,„-  .         .,  ,  ,  ■  good  order,   on   board   the   C.  Vibbard 

Shipped  on  board ' 

bound  for  J\[ew    York,   the   packages 

Ijound  for_  .    marked  and  entered  as  below  : 

( 

)    Mar-hs 
(Packages \    J  &      4  doz.  boxes  Oswego  Starch. 

JAarks J  M>  °-      6  barrels  Apples. 

RoU.  B.  Smith ,  fig't. 


Business  Information,  and  Forms.  303 

Bank     D  raft. 


No.  2350. 

Auburn    <Eitn    Sauk. 

$254.  Auburn,  Feb   24,  18 '8 4 

(Pay  to  the  order  of Charles  T.  Burtis 

_. Two  Hundred   Fifty-four (Dollars. 


To  JVassau  Flank]  )  James  M.  Seymour, 

JTew  York  )  Cashier. 


Dividend     Check. 


JTew  York,  Jdaroh  12,  188//. 

XlUctjanics'    National    Bank. 

(Pay  to Charles  T.  JlUlg or  fearer, 

Four  Hundred  Fifty-eight 'Dollars, 

and  charge  to  (Dividend  JJo   35. 

_____  H.  B.  Smith, 

$408.  General  F>ook  Keeper. 


General  Form  of  Agreement. 

This  Agreement  made  the day  of between  A—  B —  of 

City  and  State  ,  of  the  first   part,  and  C —  D —  of  City  and 

State  of  the  second  part, 

WITNESSETH: — That  the  said  G D ,  party  of  the  second  part, 

in  consideration  of  the  sum  hereinafter  named,  doth  covenant  and  agree 
to  and  with  the  said  A B of  the  first  part,  that  (insert  agreement). 

And  the  said  party  of  the  first  part  doth  covenant  and  agree  to  pay  unto 
the  said  C D (insert  agreement  of  A B .) 

And  for  the  true  and  faithful  performance  of  all  agreements  above 
mentioned,  the  parties  to  these  presents  bind  themselves  each  unto  the 

other,  in  the  sum  of dollars  as  fixed  damages  to  be  paid  by  the 

failing  party. 

In  witness  whereof  we  have  hereunto  set  our  hands  and  seals  the  day 
and  year  first  above  written. 

Signed,  sealed,  and  delivered  )  A B .     (Seal. 

in  the  presence  of  \  C — D .     (Seal.) 


304  ^Appendix. 

716.  Letters  of  Credit  can  be  procured  from  Foreign 
Exchange  Bankers,  by  depositing  the  amount  in  money  or  m 
securities.  A  small  commission  is  charged  besides  the  regular 
rate  of  exchange.     (Art.  451.) 

Circular  Letter  of  Credit. 

No.  B  S6581.  New  yoRK  Feb  ^  mL 

Gentlemen : — We  request  that  you  will  have  the  goodness  to 
furnish  Mr.  Henry  R.  Rusted,  the  bearer,  whose  signature  is 
at  foot,  with  any  funds  he  may  require  to  the  extent  of  £500  (say 
Five  Hundred  Pounds  Sterling),  against  his  drafts  upon 
Messrs.  Brown,  Shipley  &  Co.,  London;  each  draft  must 

bear  the  number  (No.  »  36581)  of  this  letter,  and  ive  engage 

that  the  same  shall  meet  due  honor. 

Whatever  sums  Mr.  Husted  may  take  up,  you  will  please 
endorse  on  the  back  of  this  Circular  letter,  which  is  to  continue 
in  force  till  Feb.  22,  1885,  from  the  present  date,  Feb.  22,  188 % 
We  are  respectfully,  gentlemen, 

Your  obedient  humble  servants, 

Brown  Brothers  &  Co. 
The  Signature  of 

Henry  R.  Husted. 
To  Messieurs  the  Bankers, 
Mentioned  on  the  third  page  of  this  Letter  of  Credit. 


INSTRUMENTS     UNDER     SEAL. 

717.  A  Contract  is  a  formal  bargain  made  between  two  or 
more  persons,  upon  sufficient  consideration,  to  do  or  not  to  do 
some  act  which  shall  be  lawful. 

718.  A  Deed  is  a  writing  or  instrument  signed,  sealed, 
and  delivered.  As  generally  used,  it  is  for  the  conveyance  of 
property. 

719.  A  Bond  is  a  sealed  obligation  for  the  payment  of 
money,  and  usually  has  a  penalty  annexed  in  case  of  failure  to 
comply  with  the  conditions  annexed. 


Book  Accounts.  305 

720.  Ground  Rents  are  leases  of  building  lots,  the  rents  of 
which  are  considered  equal  to  the  int.  on  the  value  of  the  land. 

Note. — Bonds  and  Mortgages  on  real  estate,  and  Ground  Rents  are 
regarded  with  a  good  degree  of  favor  as  investments. 

721.  A  Fee-Simple  interest  is  absolute  ownership  in  an  estate. 

722.  A  Ground  Rent  Deed  conveys  land  with  a  reservation 
of  a  specified  sum  of  money  in  the  nature  of  rent  to  be  paid  at 
stated  times,  and  may  be  for  life,  for  a  term  of  years,  or  in  fee. 

Notes. — 1.  Instruments  under  seal  are  not  barred  by  the  statute  of  limita- 
tions like  ordinary  debts. 

2.  In  ordinary  cases  where  the  consideration  is  expressed,  there  is 
no  difference  between  an  agreement  under  seal  or  otherwise,  except  that 
the  former  can  be  more  easily  proved  and  is  therefore  to  be  preferred. 


BOOK    ACCOUNTS. 

723.  In  order  to  collect  a  debt  on  the  evidence  of  a  book 
account,  a  full  copy  of  the  account  must  be  made  out,  and  it 
must  be  accompanied  with  an  affidavit,  as  follows : 

Form   of  Affidavit  for   Goods  Sold  and  Delivered. 


State  of 


County  of 


Henry  Smith  of  being  duly  sworn  (or  affirmed),  deposes  and 

says,  that  James  Brown  of ,  County  of ,  and  State  of , 

is  justly  and  truly  indebted  unto  him,  the  deponent,  in  the  sum  of 

dollars,  for  goods  sold  and  delivered  by  him  to  the  said  James  Brown  ; 
and  that  he  has  given  credit  to  the  said  James  Brown  for  all  payments 
and  set-offs  to  which  he  is  entitled  ;  and  that  the  balance  claimed,  accord- 
ing to  the  foregoing  account,  is  justly  due;  and  that  the  said  account  is 
correctly  stated. 

Sworn  and  subscribed  this day  of ,  a.  d.,  1884,  before  me 

Charles  C.  Jones, 
Commissioner  for  the  State  of . 

724.  Items  and  dates  should  be  given  in  the  account,  as  a 
general  charge  cannot  be  sustained  by  evidence  of  this  kind. 
The  entry  must  be  made  in  form  at  the  date  of  purchase  for 
the  purpose  of  charging  the  debtor,  not  as  a  mere  memo- 
randum. 

20 


306 


Appendix. 


Note. — In  order  to  be  admissible  as  evidence,  entries  should  be  made 
without  alteration,  erasure,  or  interlineation,  and  by  a  person  authorized 
to  attend  to  that  department. 

The  Statute  of  Limitations  of  the   United  States. 


725.  The  time  within  which  suit  must  be  commenced  for 
the  collection  of  a  debt,  varies  in  different  classes  of  cases  from 
one  to  twenty  years,  and  differs  in  different  States.* 

For  accounts  m  general  it  begins  from  the  date  of  the  last 
item  or  payment,  and  in  every  case  the  time  is  renewed  by 
every  partial  payment. 


States  and  Terri- 
tories. 


Alabama  ... 
Arkansas . . . 

Arizona 

California... 
Colorado  — 
Connecticut 

Dakota 

Delaware  . . . 


Dist.  of  Columbia 

Florida 

Georgia 

Tdabo 

Illinois 

Indiana 

Iowa 

Kansas 

Kentucky 

Louisiana 

Maine 

Maryland 

Massacbusetts  . . . 

Michigan 

Minnesota 

Mississippi 


6 

< 

a 

o 
o, 

O 

11 

if 

a 

Yrs. 

1 

bo 

"2 

Yrs. 

Yrs. 

Yrs. 

3 

6 

10 

20 

3 

5 

5 

10 

2 

4 

4 

5 

2 

4 

4 

5 

6 

6 

6 

3 

6 

6 

17 

17 

6 

6 

20 

20 

3 

6 

20 

20 

3 

3 

12 

12 

4 

5 

20 

20 

4 

6 

20 

2 

4 

4 

5 

5 

10 

10 

20 

6 

10 

20 

10 

5 

10 

10 

20 

3 

5 

5 

15 

5 

15 

15 

15 

3 

5 

10 

10 

6 

6 

20 

20 

3 

3 

12 

12 

6 

6 

20 

20 

G 

6 

10 

10 

6 

6 

10 

10 

3 

6 

7 

7 

States  and  Terri- 
tories. 


Missouri 

Montana.  .. 
Nebraska  . . . 

Nevada 

New  Hampshire 

New  Jersey 

New  Mexico  . . . 

New  York 

North  Carolina. 

Ohio 

Oregon 

Pennsylvania  . . 
Rhode  Island. . . 
South  Carolina. 

Tennessee 

Texas 

Utah 

Vermont 

Virginia 

Washington .... 

W.  Virginia 

Wisconsin 

Wyoming 


Yrs. 
5 

B 

4 

2 


O  a 


Yrs. 

10 

10 

5 


Yrs. 
10 
10 

5 

4 
20 
16 

6 
20 
10 
15 
10 
20 
20 
20 
10 

4 

4 

8 
20 

6 
10 
20 

5 


Yrs. 
20 
10 

5 

5 

20 
20" 
15 
20 
10 
15 
10 


Notes.— 1.  In  the  States  of  Kentucky  and  Virginia  a  store  account 
may  run  two  years.     In  W.  Va.  3  years. 

2.  In  the  case  of  notes,  etc.,  if  the  debtor  at  any  time  makes  a  written 
acknowledgment  of  indebtedness,  the  claim  is  renewed. 


*  Clark's  Commercial  Law. 


Stock  Clearing  Houses. 


307 


STOCK     CLEARING-    HOUSES. 

726.  A  Stock  Clearing  House  is  an  association  of  dealers, 
to  facilitate  the  balancing  of  transactions  in  Stocks  or  Bonds. 

Note. — Stock  Clearing  Houses  are  in  successful  operation  in  some  of 
the  large  cities  of  Europe.  An  attempt  was  made  to  establish  one  in 
New  York,  which  was  partially  successful.  The  following  is  a  glimpse 
of  the  plan  proposed : 

727.  Each  member  reports  to  the  Clearing  House  on  a  blank 
form,  the  names  of  parties  with  whom  he  has  had  dealings, 
and  the  balances  in  his  favor  or  against  him,  of  all  transactions. 

At  12 :  30  the  clerks  in  the  Clearing  House  tabulate  all  the 
balances  as  reported,  and  notify  each  member  from  whom  he 
will  receive,  or  to  whom  he  will  deliver  the  stocks  shown  by 
his  report. 

Note. — A  settling  price  is  fixed  by  the  Clearing  House  for  each  stock, 
and  members  are  required  to  receive  only  as  many  shares  of  any  stock  as 
they  may  have  bought  more  than  they  have  sold.  The  difference  between 
the  "settling  price"  and  the  buying  or  selling  prices  of  the  original 
transactions  must  be  paid  in  cash. 


The  followir 

ig  is  the  form  ol 

a  Report 

to  the  Clearing  House : 

To  Receive. 

To  Deliver. 

Balance. 

U.  P. 

N.Y.C. 

Name. 

U.  P. 

N.Y.C. 

To  Receive.         To  Deliver. 

750 

500 

J.  G.  Hewitt 

C.  T.  Burtis 

800 
Chas.  S 

100 
.Andr 

evvs. 

U.  P.          50 
400     N.  Y.  0. 

800 

300 

Chas.  S.  Andrews. . 
J.  G.  Hewitt 1 

I    500  1 
i  1000  1          1 

C.  T.  Burtis. 

TJ.  P.        200 

N.  Y.  C     200 

1000 

100 

C.  T.  Burtis 

Chas.  S.  Andrews..! 

1     300  | 
1    750  1 

J.  G.  Hewitt. 

250        U.  P. 

N.  Y.  C.      200 

Explanation. — These  three  reports  show  that  2550  shares  of  TJ.  P. 
Railroad  Stock  and  900  shares  N.  Y.  Central  were  bought  and  sold ;  but 
the  transactions  are  settled  through  the  Clearing  House  by  the  delivery  of 
400  shares  of  N.  Y.  C.  stock  and  250  shares  of  U.  P.  stock. 

Thus,  Andrews'  balance  shows  that  he  is  to  receive  400  N.  Y.  C,  Burth 
and  Hewitt  each  report  balances  of  200  N.  Y.  C.  to  deliver.  They  are 
notified  by  the  Clearing  House  to  deliver  to  Andrews. 


308  Appeiidkc. 


728o     Abbreviations  used  in   Stock  Quotations. 

Ad Adjustments. 

Allts Allotments.    Applied  to  shares  giving  the 

privilege  of  others,  at  specified  prices. 

As , Assented. 

U.  S.  c.  3's,  or  4's U.  S.  currency  bonds  at  3%  or  4%  int. 

B.  c Between  calls. 

B.  30 Buyer's  option  at  30  d. 

B.  20,  flat Buyer's  option  at  20  d.  without  interest. 

Bds.,  or  b Bonds. 

"  C  "  before  price Cash. 

Certs Certificates. 

Com Common  stock. 

Cons.,  or  en Consolidated. 

Conv.,  or  cv Convertible.     May  be  exchanged. 

Coup. ,  or  c Coupon. 

Cur.,  or  c Currency. 

Deb Debentures. 

D.  s.  f.  5's Deb.  secured  by  sinking  fund,  at  5%  int. 

Div Dividend. 

Ex.  d.,  or  e.  d Without  dividend. 

Ex.  coup Without  coupon. 

Ext Extended. 

Fd Funded. 

Gen General. 

Gtd Guaranteed. 

L.  g Land  grants. 

L.,  or  1 Lot,  the  aggregate  of  several  sales. 

L.  s Land  Scrip. 

Inc.  6's Income  bonds,  at  6%  interest. 

Mort.,  or  m Mortgage. 

N.  6's New  Q%  bonds. 

Pref.,  or  pf  Preferred. 

Pur.  m.  fd Purchase  money  funded. 

Reg.,  or  r Registered. 

R.  e . .  Registered  and  extended. 

Sep Scrip. 

S.  30 Seller's  option  at  30  days. 

S.  F.,  or  s.  f Sinking  fund. 

W.  n Without  notice. 

2d  M.  s.  f .  7's  '85 Sinking  fund  bonds  secured  by  2d  mort., 

payable  at  7%  in  1885. 
Con.  M,  &  s.  f.  6's Consolidated  mort.  and  sinking  fund,  at  6%. 


V|S^— '       ■*■■■♦ 

1 ISOELL  AKEOTJS  JP|XAMPLES. 


1.  What  number  is  that  to  which  if  16  be  added,  then  25  subtracted 
from  the  sum,  the  difference  be  multiplied  by  21,  and  the  product  divided 
by  28,  the  quotient  will  be  63  ? 

2.  How  many  gills,  pints,  and  quarts,  of  each,  an  equal  number,  are 
there  in  a  hogshead  ? 

3.  A  company  of  175  men  have  provisions  enough  to  last  6  months  ; 
if  47  of  them  leave,  how  long  will  the  same  provisions  last  those  that 
remain  ? 

4.  A  farmer  had  45  head  of  cattle,  and  hay  enough  to  last  them  5| 
months ;  if  he  buys  13  head  more,  how  long  will  the  same  hay  last  the 
whole  ? 

5.  Six  men  bought  a  ship  together  worth  $45268,  for  which  A  paid  \ 
of  the  whole,  B  \,  and  the  others  paid  the  balance  equally ;  how  much 
-did  each  pay  ? 

6.  A  manufacturer  hired  an  equal  number  of  men,  women,  and 
children,  at  75  cts.,  62|  cts ,  and  37^  cts.  each  per  day,  and  the  daily 
wages  of  the  whole  amount  to  $113.75  ;  how  many  of  each  class  did  he 
employ  ? 

7.  A  man  bought  a  drove  of  horses  for  $17947,  and  after  selling  62  of 
them,  at  $83  apiece,  the  remainder  netted  him  $51  each ;  how  many  did 
he  buy,  and  for  how  much  apiece  must  he  sell  them  to  make  $2510  by 
the  operation  ? 

8.  A  merchant  bought  868  yards  of  cloth  at  $6.50  a  yard ;  he  after- 
wards sold  253  yards  at  $5|  per  yard  to  one  customer,  and  368  yards  at 
$8]  to  another  ;  how  many  yards  had  he  left,  and  what  was  the  net  cost 
to  him  ? 

9.  A  man  bought  148  acres  of  land,  at  $23  per  acre,  and  260  acres  at 
$17 ;  he  afterwards  sold  300  acres  at  $25  ;  how  many  acres  had  he  left, 
and  what  did  it  stand  him  in  per  acre  ? 

10.  A  garrison  of  450  men  has  provisions  for  5  months  ;  how  many 
must  be  discharged,  that  the  same  provisions  may  last  71  months? 

11.  In  a  certain  county  are  105260  topers,  who  drink  3  glasses  of  liquor 
apiece  every  day,  at  a  cost  to  them  of  8  cents  a  glass ;  how  many  barrels 
of  flour  would  this  useless  expense  pay  for,  per  annum,  when  flour  is  $8 
a  barrel  ? 


310  Miscellaneous  Examples. 

12.  A  grocer  having  bought  1328  pounds  of  butter  at  27*  cents  a  pound, 
afterwards  sold  263  pounds  at  28f  cents,  and  375  pounds  at  29|  cents  ;  how 
much  had  he  left,  and  what  must  he  get  for  it  in  order  to  gain  $215  by 
the  operation  ? 

13.  A  drover  brought  1463  sheep,  and  285  lambs  to  market,  the  former 
costing  him  $5.15  per  head,  and  the  latter  $2.17  per  head  ;  having  sold 
320  sheep  and  lambs  together  at  $5|  a  head,  he  wishes  to  know  at  what 
price  per  head  he  must  sell  the  remainder  in  order  to  gain  20%  on  the 
money  invested. 

14.  A  man  bought  a  lot  of  silver  containing  tea-spoons,  dessert-spoons, 
and  table-spoons,  of  each  an  equal  number,  weighing  respectively  5  pwt. 
6  gr. ;  13  pwt.  10  gr. ;  and  1  oz.  11  pwt.  8  gr. ;  the  weight  of  the  whole 
was  6  lb.  8  oz. ;  how  many  spoons  were  there  of  each  kind? 

15.  A  man  bought  a  drove  consisting  of  cows,  calves,  and  oxen,  in 
equal  numbers,  for  $3693.375  ;  for  cows  he  gave  $27i  apiece,  for  calves 
$4^,  and  for  oxen  $43f  ;  how  many  were  there  of  each  kind  ? 

16.  A  liberty  pole  108  ft.  high  was  broken  in  such  a  manner  that  its 
top  struck  the  ground  36  ft.  from  its  foot,  the  other  end  resting  on  the 
top  of  the  part  left  standing ;  how  high  from  the  ground  was  it  broken. 
(Art.  704.) 

17.  A  man  pays  $1500  per  annum  interest  on  various  mortgages,  at 
Ifo  ;  how  much  money  does  he  hire? 

18.  What  must  be  the  face  of  a  note  to  cover  the  discount  for  90  d.,  at 
6%,  and  yield  $472.86? 

19.  A  man  spent  |  and  £  of  his  money  and  $20  besides,  when  he  had 
$80  left ;  how  much  had  he  at  first  ? 

20.  A  barn  was  38  ft.  wide  at  the  gable  ends,  and  the  ridge  of  the 
roof  was  5  ft.  above  the  eaves  ;  how  many  ft.  of  boards  would  cover  the 
gable  ends  ? 

21.  Sold  goods  for  $2543.50  at  a  profit  of  5%,  and  took  a  note  at  60  d., 
which  was  discounted  the  same  day,  at  6%  per  annum;  what  was  the 
net  profit  ? 

22.  Which  is  the  better  investment,  U.  S.  3's,  at  103|,  or  Bait.  &  O. 
1st  6's  1919,  atll4i? 

23.  Bought  Boston  H.  &  E.  1st  M.  7's  due  in  1900,  at  114;  what  is  the 
per  cent  income  on  the  investment  ? 

24.  What  is  the  weight  of  an  iron  cylinder  15  ft.  long  and  10  in.  in 
diameter,  allowing  4  cu.  in.  to  a  pound  ? 

25.  A  man  having  a  triangular  gore  of  land,  one  side  of  which  was  256 
rods  long,  and  the  perpendicular  distance  from  this  side  to  the  opposite 
corner,  72  rods,  exchanged  it  for  a  square  farm  of  equal  area ;  what  was 
the  side  of  his  farm  ? 


Miscellaneous  Examples.  311 

26.  An  importer  bought  1565  yards  of  silk,  at  5s.  Gd.  per  yard  ;  paid 
£7  12s.  for  freight,  25  per  cent  duties,  and  remitted  a  bill  on  London  at 
9£  per  cent  premium ;  how  must  he  sell  it  per  yard  on  6  months,  jn  order 
to  make  12^  per  cent,  allowing  7  per  cent  interest  ? 

27.  A  merchant  sent  his  agent  in  London  425  bales  of  cotton  weighing 
356  pounds  apiece,  which  cost  him  9|  cents  a  pound  ;  the  agent  paid  f  d.  a 
pound  for  freight,  £43  for  cartage,  sold  it  at  8d,  a  pound,  and  charged 
2h  per  cent  commission.  If  the  merchant  sells  a  bill  of  exchange  for  the 
amount,  at  10|% ,  will  he  make  or  lose  by  the  operation.     How  much  ? 

23.  "What  rate-per  cent  income  will  be  realized  from  8%  stock  bought 
at  95,  if  paid  at  par  in  20  yr.? 

29.  Four  notes  of  $500  each  are  due  in  3,  6,  9,  and  12  months  respec- 
tively ;  in  how  many  months  may  they  all  be  paid  at  one  time  ? 

30.  Which  is  the  greater,  an  income  of  $500  per  annum  for  15  years  to 
come,  or  the  reversion  in  perpetuity  of  $500  annuity  at  the  end  of  15  years, 
interest  at  6  per  cent  ? 

31.  Which  is  the  better  investment,  7%  bonds,  or  a  house  which  rents 
for  $240  a  year,  taxes  being  $30.50,  and  annual  repairs  $40  ? 

32.  What  is  the  average  distance  between  stations  on  a  R.  R.  that  is 
149  m.  234  r.  4  yd.  2  ft.  long,  the  number  of  stations  being  18  including 
one  at  each  end  of  the  road  ? 

33.  How  must  goods  which,  cost  60  cents  a  yard  be  marked,  that  the 
merchant  may  discount  20%  from  the  price  and  still  make  20%  ? 

34.  How  many  shares  of  mining  stock  at  80  must  be  sold,  that  the 
proceeds  invested  in  Iowa  Mid.  1st  M.  8's,  due  in  1900,  may  yield  a  profit 
of  $960  if  bought  at  108  ? 

35.  A  father  left  an  estate  valued  at  $11740  to  3  sons,  whose  ages  were 
15,  13,  and  11  respectively,  to  be  so  divided  that  if  put  at  interest  at  5%, 
the  amount  should  be  equal  as  the  sons  came  of  age  ;  what  sum  did  he 
will  to  each  ? 

36.  Bought  $600  worth  of  books  at  a  discount  of  33^%  from  list  prices, 
and  sold  them  at  regular  retail  price  on  6  mo.  credit ;  what  was  the  per 
cent  profit,  if  money  was  worth  6%  ? 

37.  What  must  I  pay  to  insure  a  factory  valued  at  $21000  at  £  %;  and 
the  machinery  valued  at  $15400  at  f  %  ? 

38.  Sold  a  bill  of  goods  amounting  to  $1875,  of  which  15%  was  payable 
in  cash,  25%  in  3  mo.,  20%  in  4  mo.,  and  the  balance  in  6  months  ;  how 
much  cash  would  pay  the  debt  at  once,  when  money  is  6*%  per  annum  ? 

39.  A  miller  had  400  barrels  of  flour  worth  $6£  a  barrel,  15%  ©f  it  was 
destroyed  by  a  freshet ;  he  sold  the  remainder  at  $8.50  a  barrel  ;  how 
much  did  he  gain  or  lose  ? 

40.  Which  is  the  more  profitable  investment,  to  buy  flour  at  $8.50  a  bar- 
rel on  a  credit  of  6  months,  or  at  $8.25  on  2  mo.  when  money  is  worth  6%? 


312  Miscellaneous  Examples. 


41.  A  cylindrical  tank  30  ft.  in  diameter  and  15  ft.  deep  is  filled  with 
oil ;  how  many  gallons  does  it  contain  and  what  is  its  value  at  4$  cents  a 
gallon  ? 

42.  A  merchant's  retail  price  yields  a  profit  of  25%  ;  if  he  discounts 
10%  at  wholesale,  what  per  cent  does  he  gain  at  wholesale? 

43.  Bought  Chesapeake  &  Ohio  1st  pf.  R.  R.  Stock  for  26^,  the  same 
Stock  sold  last  year  for  32£  ;  how  much  would  a  man  lose  who  bought 
$5000  worth  last  year  ? 

44.  At  what  price  must  6  %  bonds  payable  in  10  years  be  bought  to 
realize  8£%  on  the  investment? 

45.  What  is  the  per  cent  income  in  1884  on  Chic.  R.  I.  &  Pac.  6's  coup., 
payable  at  par  in  1917,  bought  at  123£  ? 

46.  Divide  $1860  among  A,  B,  and  C,  so  that  for  every  $5  given  to  A, 
B  may  receive  $4,  and  for  every  $3  given  to  B,  C  may  receive  $1. 

47.  Divide  §  into  two  parts,  so  that  one  of  them  is  greater  than  the 
other  by  f . 

48.  A  mine  is  worth  $50000  ;  a  person  sold  T3<r  of  his  share  for  $3750  • 
what  part  of  the  mine  did  he  own  ? 

49.  A  can  do  as  much  work  in  2  days,  as  B  can  do  in  3  days,  together 
they  did  a  certain  job  in  12  days;  in -what  time  would  A  alone  have 
done  it  ?    In  what  time  would  B  ? 

50.  A  piece  of  land  is  95£  r.  long,  and  58|  r.  wide  ;  how  many  house 
lots  of  equal  size,  the  largest  possible,  can  be  made  from  it  ? 

51.  When  stock  originally  worth  $4000,  sells  for  $4250,  what  is  the 
per  cent  premium  ? 

52.  In  1870  the  population  of  Chicago  was  298977,  which  was  1905 
more  than  f  the  population  of  Brooklyn.  What  was  the  population  of 
Brooklyn  at  that  time  ? 

53.  The  population  of  Brooklyn  in  1880  was  566663,  that  of  Chicago 
503185 ;  what  was  the  %  gain  of  each  ? 

54.  The  population  of  New  York  in  1870  was  942292  ;  in  1880  it  was 
1206299  ;  what  per  cent  was  the  gain  ? 

55.  What  principal  on  interest  from  March  1,  1880  to  Nov.  1,  1884,  at 
6%,  will  amount  to  $4401.60? 

56.  A  merchant  sells  a  quantity  of  goods  at  such  a  price  that  |  of  the 
selling  price  will  cover  the  cost ;  what  is  his  gain  per  cent  ? 

57.  The  crown  of  a  certain  king  consisted  of  gold  and  silver  in  the 
ratio  of  2  : 1 ;  what  was  the  per  cent  of  each  ? 

58.  A  bookseller  has  150  books  to  pack  in  two  boxes,  whose  dimensions 
are  as  follows :  the  larger  one  4|  feet.,  2  ft.  8  in.,  and  2  ft. ;  the  smaller 
4  ft.,  2£  ft.,  and  1|  ft.;  in  the  smaller  he  can  pack  50  books  ;  how  many 
will  remain  unpacked  when  he  has  filled  both  boxes,  the  books  being 
of  the  same  size  ? 


Miscellaneous  Examples.  313 

59.  American  gold  coin  contains  1  oz.  alloy  to  9  oz.  pure  gold ;  what 
quantity  of  each  will  a  ton  of  double  eagles  contain  ? 

60.  Divide  the  number  7980  into  3  parts  in  the  proportion  of  5,  7,  and  9. 

61.  An  Iron  Manufacturing  Co.  made  an  assessment  of  6%  on  its 
capital  stock,  par  value  $50 ;  how  much  must  a  man  pay  who  owned 
18000  shares  of  stock  ? 

62.  A  father  dividing  his  estate  between  2  sons,  gave  the  younger 
$2800,  which  was  75%  of  the  share  of  the  elder  ;  what  was  the  amount  of 
his  estate  ? 

63.  25260  is  20%  more  than  what  number? 

64.  Sold  2  droves  of  cattle  for  $11360  a  piece ;  on  one  I  gained  12^%, 
on  the  other  lost  8%  ;  required  the  cost  of  each  drove,  and  the  net  gain  % 
on  the  transaction. 

65.  Sold  goods  for  $450  and  made  25%  ;  what  per  cent  should  I  Rave 
made  had  I  sold  them  for  $6)0 ? 

66.  Paid  $8.40  apiece  for  dictionaries ;  becoming  shop-worn,  deducted 
25%  from  the  marked  price,  and  yet  made  10%  profit;  required  the 
marked  price? 

67.  What  length  of  paper  f  yd.  wide  will  cover  a  wall  15  ft.  8  in.  by 
11  ft.  3  in.? 

68.  Find  the  circumference  of  a  wheel  whose  diameter  is  4  ft.  8  in.; 
how  many  times  will  it  turn  round  in  10£  miles  ? 

69.  A  dealer  bought  6  hectars  of  land  for  $1050,  and  divided  it  into  lots 
of  8  ars  each  ;  what  must  be  the  price  per  lot  to  gain  30%  ? 

70.  A  note  of  $600  was  given  Jan.  1,  at  6%  interest,  on  which  a  pay- 
ment of  $225  was  made  July  3.  Oct.  15,  the  note  was  bought  at  3  % 
discount  on  its  value  at  that  time  ;  how  much  was  paid  for  it  ? 

71.  |  of  C's  money  and  f  of  D's  equal  $900  ;  and  f  of  D's  is  twice  f  of 
C's  money ;  what  sum  has  each  ? 

72.  In  how  many  days  will  $75  at  7T3¥%  int.  gain  80  cents  ? 

73.  A  note  of  $800  dated  Jan.  1,  1881,  had  an  indorsement  June  4, 
1881,  of  $250,  and  Oct.  9,  '81,  $120 ;  what  was  due  Apr.  26,  '82,  interest 
being  6%  ? 

74.  A  man  owes  $12000,  of  which  \  is  due  in  5  mo.,  \  in  9  mo.,  and  the 
remainder  in  15  mo.;  what  is  the  present  worth  of  the  debt? 

75.  The  true  discount  of  a  debt  of  $1215  due  in  10  mo.  20  d.  is  $90 ; 
what  is  the  rate  ? 

76.  What  is  the  interest  in  United  States  money  on  £167  8s.  3d  ,  at 
7T3^%,  from  June  10,  '81,  to  May  2,  '82  ? 

77.  Sold  a  cow  so  that  -f  of  the  gain  was  equal  to  T^  the  cost ;  what 
was  the  gain  %  ? 


314  Miscellaneous  Examples. 


78.  A  father  wills  an  estate  of  #19000  as  follows  :  to  each  of  3  sons  he 
gives  $1000  more  than  to  his  daughter,  and  to  his  widow  $1000  more  than 
to  all  the  children ;  what  is  the  share  of  each  ? 

79.  A  storehouse  takes  fire  in  which  A  has  350  bbl.  of  flour,  worth  $8.25 
a  bbl.;  B  has  275  bbl.,  worth  $9  a  bbl.;  and  C  has  2500  bushels  of  corn, 
worth  $1.10  a  bu.;  the  damaged  flour  and  grain  are  sold  all  together  for 
•$3100 :  how  shall  this  be  divided  between  A,  B,  and  C ;  what  is  each  man's 
actual  loss,  and  his  loss  per  cent  ? 

80.  What  is  the  difference  in  value  of  two  pieces  of  land  one  of 
which  is  87  ft.  by  42  ft.,  the  other  57  ft.  square,  both  being  worth  $1.75  a 
square  foot? 

81.  Find  the  cash  balance  of  the  following  account: 

Jones  Bros,  in  account  with  Loeser  &  Co. 

Dr.  Apr.  10,  1884,  to  mdse.  $150;  Apr.  30,  $400;  May  16,  $90;  May 
24,  $100  ;  June  1,  $300  ;  June  10,  $340;  June  26,  $200. 

Or.  Apr.  12,  1884,  cash  $250  ;  May  1,  $180  ;  June  7,  $400 ;  June  25, 
$564.  If  the  acct.  is  settled  July  1,  1884,  what  will  be  the  true  balance 
allowing  each  item  to  draw  interest  from  its  date,  at  6  per  cent  ? 

82.  The  duty  on  a  quantity  of  coffee  in  bags  containing  185  lbs.  each, 
value  14  cts.  a  pound,  was  $3591.75;  the  duty  at  30%,  tare  5%  ;  how 
many  bags  were  imported  ? 

83.  The  taxable  property  of  a  village  is  $860000,  the  number  of  polls 
at  $1.50  each  is  620 ;  a  Union  School -house  is  to  be  built,  worth  $22860.25; 
allowing  3  %  for  collecting,  what  will  be  the  tax  rate  ? 

84.  What  tax  will  a  man  be  required  to  pay  whose  property  is  valued 
at  $16420,  and  who  pays  for  2  polls  ? 

85.  A  Milwaukee  grain  dealer  invested  as  follows  :  800  bu.  red  wheat, 
at  $1.30;  500  bu.  white,  at  $1.60;  and  300  bu.  spring  wheat,  at  $1.20. 
The  whole  was  shipped  to  his  agent  in  New  York,  who  sold  the  first,  at 
15$>  advance;  the  second,  at  20%  advance;  and  the  third  at  $1.15  a 
bushel;  his  expenses  were  $112.25,  his  commission  3%;  what  were  the 
net  proceeds  ? 

86.  In  the  above  speculation,  what  per  cent  was  the  grain  dealer's 
gain? 

87.  A  merchant  sells  goods  at  different  times  as  follows:  May  2,  a  bill 
of  $800  on  4  mo.;  May  15,  a  bill  of  $1200  on  6  mo. ;  June  1,  a  bill  of  $1500 
on  8  mo. ;  and  June  15,  $800  for  cash  ;  he  then  agrees  to  take  a  note  for 
the  whole,  at  60  days  with  interest  ;  what  should  be  the  date  of  the  note  ? 

88.  March  4,  1884,  a  note  for  $1000,  at  6%  interest,  was  given,  on 
which  the  following  indorsements  were  afterwards  made:  May  1,  1884, 
$75;  July  17,  1884,  $15.50;  Dec.  1,  1884,  $30.50;  Dec.  31,  1884,  $400; 
Jan.  31,  1835,  $250  ;  what  was  due  Aug.  18,  1885  ? 


Appendix. 


315 


TABLE    I. 

THE  AMOUNT  OF  AN  ANNUITY  OF   $1,  AT  COMP.  INT.,  FROM   1   YR.  TO  50. 


Yr. 
1 

3  per  ct. 

%%  per  ct. 

4  per  ct. 

5  per  ct. 

6  per  ct. 

7  perct. 

Yr. 

1.000000 

1.000000 

1.000000 

1.000000 

1.000000 

1.000000 

1 

2 

2.030000 

2.035000 

2.040000 

2.050000 

2.060000 

2.070000 

2 

3 

3.090900 

3.106225 

3.121600 

3.152500 

3.183600 

3.214900 

3 

4 

4.183627 

4.214943 

4.240464 

4.310125 

4.374616 

4.439943 

4 

5 

5.309136 

5.362466 

5.416322 

5.525631 

5.637093 

.  5.750739 

5 

6 

6.468410 

6.550152 

6.632975 

6.801913 

6.975319 

7.153291 

6 

7 

7.662402 

7.779408 

7.898294 

8.142003 

8.393838 

8.654021 

7 

8 

8.892336 

9.051687 

9.214226 

9.549109 

9.S97468 

10.259803 

8 

9 

10.159106 

10.368496 

10.582795 

11.026564 

11.491316 

11.977989 

9 

10 

11.463879 

11.731393 

12.006107 

12.577893 

13.180795 

13.816448 

10 

11 

12.807796 

13.141992 

13.486351 

14.206787 

14.971643 

15.783599 

11 

12 

14.192029 

14.601962 

15.025805 

15.917127 

16.869941 

17.888451 

12 

13 

15.617790 

16.113030 

16.626838 

17.712983 

18.882138 

20.140643 

13 

14 

17.086324 

17.676986 

18.291911 

19.598632 

21.015066 

22.550488 

14 

15 

18.598914 

19.295681 

20.023588 

21.578564 

23.275971 

25.129022 

15 

16 

20.156881 

20.971030 

21.824531 

23.657492 

25.672528 

27.888054 

16 

17 

21.761588 

22.705016 

23.697512 

25.840366 

28.212880 

30.840217 

17 

18 

23.414436 

24.499691 

25.645413 

88.132886 

30.905653 

33.999033 

18 

19 

25.416868 

26.357180 

27.671229 

30.539004 

83.759992 

37.378965 

19 

20 

26.870374 

28.279682 

29.778078 

33.065954 

30.785592 

40.995492 

20 

21 

28.676486 

30.269471 

31.969202 

35:719252 

39.992727 

44.865177 

21 

22 

30.536780 

32.328902 

34.247970 

38.505214 

43.392290 

49.005739 

22 

23 

32.452884 

34.460414 

36.617889  • 

41.4:30475 

46.995828 

53.436141 

23 

24 

34.426470 

36.666528 

39.082604 

44.501999 

50.815577 

58.176671 

24 

25 

36.459264 

38.949857 

41.645908 

47.727099 

54.864512 

63.249030 

25 

26 

38  553042 

41.313102 

44.311745 

51.113454 

59.156383 

68676470 

26 

27 

40.709634 

43.759060 

47.084214 

54.66'.n26 

63.705706 

74.483823 

27 

28 

42.930928 

46.290627 

49.967583 

58.402583 

68.528112 

80.697691 

28 

29 

45.218850 

48.910799 

52.966286 

68.822719 

73.639798 

87.346529 

29 

30 

47.575416 

51.622677 

56.084938 

66.438847 

79.058186 

94.460786 

30 

31 

50.002678 

54.429471 

59.328335 

70.760790 

84.801677 

102.073041 

31 

32 

52.502759 

57.334502 

62.701469 

75.298829 

90.889778 

110.218154 

32 

33 

55.077841 

60.341210 

66.209527 

80.063771 

97343165 

118.933425 

33 

34 

57.7:30177 

63.453152 

69.857909 

85.066959 

104.183755 

128.258765 

34 

33 

60.462082 

66.674013 

73.652225 

90.320307 

111.434780 

138.236878 

35 

36 

63.275944 

70.007603 

77.598314 

95.836323 

119.120867 

148.913460 

36 

37 

66.174223 

73.457869 

81.702246 

101.628139 

127.268119 

160.337400 

37 

38 

69.159449 

77.028895 

85.970336 

107.709546 

135.904206 

172.561020 

38 

39 

72.234233 

80.724906 

90.409150 

114.095023 

145.058458 

185.640292 

39 

40 

75.401260 

84.550278 

95.025516 

120.790774 

154.761966 

199.635112 

40 

41 

•  78.663296 

88.509537 

99.826536 

127.839763 

165.047684 

214.609570 

41 

42 

82.023196 

92.607371 

104.819598 

135.231751 

175.950545 

230.632240 

42 

43 

85.483892 

96.848629 

110.012.382 

142.993:339 

187.507577 

247.776496 

43 

44 

89.048409 

101.238331 

115.412877 

151.143006 

199.758032 

266.120851 

44 

45 

92.719861 

105.781673 

121.029392 

159.700156 

212.743514 

285.749311 

45 

46 

96.501457 

110.484031 

126.870568 

168.685164 

226.508125 

306.751763 

46 

47 

100.396501 

115.350973 

132.945390 

178.119422 

241.098612 

329.224386 

47 

48 

104.408396 

120.388257 

139.263206 

188.025393 

256.564529 

353.270093 

48 

49 

I  10S.540648 

125.601846 

145.833734 

198.426663 

272.958401 

378.999000 

49 

50 

!  112.796867 

130.997910 

152.667084 

209. 34?  996 

290.335905 

406.528929 

50 

316 


Annuities, 


TABLE    II. 

THE  PEESEXT  WORTH  OF  AN  ANNUITY  OP   $1,  PROM  1   YEAR  TO  50. 


Yr. 
1 

3  per  ct. 

3l/3  perct. 

4  per  ct. 

5  per  ct. 

6  per  ct. 

7  per  ct. 

Yr. 

0.97087 

0.96618 

0.96154 

0.95238 

0.94339 

0.934579 

1 

2 

1.91347 

1.89969 

1.88609 

1.85941 

1.83339 

1.808017 

2 

3 

2.82801 

2.80164 

2.77509 

2.72325 

2.67301 

2.624314 

3 

4 

3.71710 

3.67308 

3.62990 

3.54595 

3.46511 

3.387207 

4 

5 

4.57971 

4.51505 

4.45182 

4.32948 

4.21236 

4.100195 

5 

6 

5.41719 

5.32855 

5.24214 

5.07569 

4.91732 

4.766537 

6 

7 

6.23028 

6.11454 

6.00205 

5.78637 

5.58238 

5.389286 

7 

8 

7.01969 

6.87396 

6.73274 

6.46321 

6.20979 

5.971295 

8 

9 

7.78611 

7.60769 

7.43533 

7.10782 

6.80169 

6.515228 

9 

10 

8.53020 

8.31661 

8.11090 

7.72173 

7.36000 

7.023577 

10 

11 

9.25262 

9.00155 

8.76048 

8.30641 

7.88687 

7.498669 

11 

12 

9.95400 

9.66333 

9.38507 

8.86325 

8.38384 

7.942671 

12 

13 

10.(53495 

10.30274 

9.68565 

9.39357 

8.85268 

8.357635 

13 

14 

11.29607 

10.92052 

10.56312 

9.89864 

9.29498 

8.745452 

14 

15 

11.93794 

11.51741 

11.11839 

10.37966 

9.71225 

9.107898 

15 

16 

12.56110 

1-2.09412 

11.65230 

10.83777 

10.10589 

9.446632 

16 

17 

13.16612 

12  65132 

12.16567 

11.27407 

10.47726 

9.763206 

17 

IS 

13.75351 

13.18968 

12.65930 

11.68959 

10.82760 

10.059070 

18 

19 

14.32380 

13.70984 

13.13394 

12.08532 

11.15812 

10.335578 

19 

20 

14.87747 

14.21240 

13.59033 

12.46221 

11.46992 

10.593997 

20 

21 

15.41502 

14.69797 

14.02916 

12.82115 

11.76408 

10.835527 

21 

22 

15.93692 

15.16712 

14.45112 

13.1(5300 

12.04158 

11.061241 

22 

23 

16.44361 

15.62041 

14.85684 

13.48857   • 

12.30338 

11.272187 

23 

24 

16.93554 

16.05837 

15.24696 

13.79864 

12.55036 

11.469334 

24 

25 

17.41315 

16.48151 

15.62208 

14.09394 

12.78336 

11.653583 

25 

26 

17.87684 

16.89035 

15.98277 

14.37518 

13.00317 

11.825779 

26 

27 

18.32703 

17.28536 

16.32959 

14.64303 

13.21053 

11.986709 

27 

28 

18.76411 

17.66702 

16.66306 

14.89813 

13.40616 

12.137111 

28 

29 

19.18845 

18.03577 

16.98371 

15.14107 

13.59072 

12.277674 

29 

30 

19.60044 

18.39205 

17.29203 

15.37245 

13.76483 

12.409041 

30 

31 

20.00043 

18.73628 

17.58849 

15.59281 

13.92909 

12.531814 

31 

32 

20.38877 

19.06887 

17.87355 

15.80268 

14.08404 

12.646555 

32 

33 

20.76579 

19.39021 

18.14765 

16.00255 

14.23023 

12.753790 

33 

34 

21.13184 

19.70068 

18.41120 

16.19290 

14.36814 

12.854009 

34 

35 

21.48722 

20.00066 

18.66461 

16.37419 

14.49825 

12.947672 

35 

36 

21.83225 

20.29049 

18.90828 

16.54685 

14.62099 

13.035208 

36 

37 

22.16724 

20.57053 

19.14258 

16.71129 

14.73678 

13.117017 

37 

38 

22.49246 

20.84109 

19.36786 

16.86789 

14.84602 

13.193473 

38 

39 

22.80822 

21.10250 

19.58448 

17.01704 

14.94907 

13.264928 

39 

40 

23.11477 

21.35507 

19.79277 

17.15909 

15.04630 

13.331709 

40 

41 

23.41240 

21.59910 

19.99305 

17.29437 

15.13802 

13.394120 

41 

42 

23.70136 

21.83488 

20.18563 

17.42321 

15.22454 

13.452449 

42 

43 

23.98190 

22.06269 

20.37079 

17.54591 

15.30617 

13.506962 

43 

44 

24.25427 

22.28279 

20.54884 

17.66277 

15.38318 

13.557908 

44 

45 

24.51871 

22.49545 

20.72004 

17.77407 

15.45583 

13.605522 

45 

46 

24.77545 

22.70092 

20  88465 

17.88007 

15.52437 

13.650020 

46 

47 

25.02471 

22.89943 

21.04294 

17.98102 

15.58903 

13.691608 

47 

48 

25.26671 

23.09124 

21.19513 

18.07716 

15.65003 

13.730474 

48 

49 

25.50166 

23.27656 

21.34147 

18.16872 

15.70757 

13.766799 

49 

50 

!     25.72976 

23.45562 

21.48218 

18.25593 

15.76186 

13.800746 

50 

Appendix. 


317 


TABLE    III. 

AMOUNT  OF  $1   AT  COMPOUND   INT.,   FROM   1   YEAR  TO  50. 


Yr. 

3  per  ct.  \SY2  perct. 

4  per  ct. 

5  per  ct. 

6  per  ct. 

7  per  ct. 

8  per  ct. 

Tr. 

1 

1.030000      1.035000 

1.040000 

1.050000 

1.060000 

1.070000 

1.080000 

1 

2 

1.060900  1  1.071225 

1.081600 

1.102500 

1.123600 

1.144900 

1.166400 

.2 

3 

1.09272?      1.108718 

1.124864 

1.157625 

1.191016 

1.225043 

1.259712 

3 

4 

1.125509  '<  1.147523 

1.169859 

1.215506 

1.262477 

1.310796 

1.360489 

4 

5 

1.159274     1.187686 

1.216653 

1.276282  | 

1.338226 

1.402552 

1.469328 

5 

6 

1.194052 

1.229255 

1.265319 

1.340096 

1.418519 

1.500730 

1.586874 

6 

7 

1.229874 

1.272279 

1.315932 

1.407100 

1.503630 

1.605781 

1.713824 

7 

8 

1.266770 

1 .316809 

1.368569 

1.477455 

1.593848 

1.718186 

1.85093C 

8 

9 

1.304773 

1.362897 

1.423312 

1.551328  | 

1.689479 

1.8:38459 

1.999005 

9 

10 

1.343916 

1.410599 

1.480244 

1.628895  | 

1.790848 

1.967151 

2  158925 

10 

11 

1.384234 

1.459970 

1.539454 

1.710833 

1.898299 

2.104852 

2.331639 

11 

12 

1.425761 

1.511069 

1.601032 

1.795856 

2.012196 

2.252192 

2.518170 

12 

13 

1.468534 

1.563956 

1.665073 

1.885649 

2.132928 

2.409845 

2.719624 

13 

14 

1.512590 

1.618694 

1.731676 

1.979932 

2.260904 

2.578534 

2.937194 

14 

15 

1.557967 

1.675349 

1.800943 

2.078928 

2.896558 

2.759031 

3.172169 

15 

16 

1.604706 

1.733986 

1.872981 

2.182875 

2.540352 

2.952164 

3.425943 

16 

17 

1.652848 

1.794675 

1.947900 

2.292018 

2.692773 

3.158815 

3.700018 

17 

18 

1.702433 

1.857481, 

2.025816 

2.406619 

2.854339 

3.379931 

3.996019 

18 

19 

1.753506 

1.922501 

2.106849 

2.526950 

3.025599 

3.616526 

4.315701 

19 

20 

1.806111 

1.989789 

2.191123 

2.653298 

3.207135 

3.869683 

4.660957 

20 

21 

1.860295 

2.059431 

2.278768 

2.785963 

3.399564 

4.140561 

5.033834 

21 

22 

1.916103 

2  131512 

2.369919 

2.925261 

3.603537 

4.430400 

5.436540 

22 

23 

1.973586 

2.206114 

2.464715 

3.071524 

3.819750 

4.740528 

5.871464 

23 

24 

2.032794 

2.283328 

2.i 563304 

3.225100 

4.048935 

5.072365 

6.341181 

24 

25 

2.093778 

2.363245 

2.665836 

3.386355 

4.291871 

5.427431 

6.848475 

25 

26 

2.156591 

2.445959 

2.772470 

3.555673 

4.549383 

5.807351 

7-96353 

26 

27 

2.221289 

2.531567 

2.883369 

3.733456 

4.822346 

6.213868 

7.988062 

27 

28 

2.287928 

2.620177 

2.998703 

3.920129 

5.111687 

6.648836 

8.627106 

28 

29 

2.356565 

2.711878 

3.118651 

4.116136 

5.418388 

7.114255 

9.3172751  29 

30 

2.427262 

2.806794 

3.243397 

4.321942 

5.743491 

7.612253 

10.062657 

30 

31 

2.500080 

2.905031 

3.373133 

4.538039 

6.088101 

8.145110 

10.867669 

31 

32 

2.575083 

3.006708 

3.508059 

4.764941 

6.4533S7 

8.715268 

11.737083 

32 

33 

2.652335 

3.111942 

3.648381 

5.003188 

6.840590 

9.325.337 

12.676049 

33 

34 

2.731905 

3.220860 

3.794316 

5.253343 

7.251025 

9.978110 

13.690134  34 

35 

2.813862 

3.333590 

3.946089 

5.516015 

7.686087 

10.676578 

14.785344 

35 

36 

2.898278 

3.450266 

4.103932 

5.791816 

8.147252 

11.423939 

15.908172 

36 

37 

2.985227 

3*71025 

4.268090 

6.081407 

8.636087 

12.223614 

17.245626 

37 

38 

3.074783 

3.696011 

4.438813 

6.385477 

9.154252 

13.079277 

18.625276 

38 

39 

3.167027 

3.S25372 

4.616366 

6.704751 

9.703507 

13.994827 

20.115298 

39 

40 

3.262038 

3.959260 

4.801021 

7.039989 

10.285718 

14.974465 

21.724522 

40 

41 

3.359899 

4.097834 

4.993061 

7.391988 

10.902861 

16.022677 

23.462483 

41 

42 

3.460696 

4.241258 

5.192784 

7.761587 

11.557033 

17.144265 

25.339482 

42 

43 

3.564517 

4.389702 

5.400495 

8.149667 

12.250455 

18.344363 

27.366640 

43 

44 

3.671452 

4.543342 

5.616515 

8.557150 

12.985482 

19.628469 

29.555972 

44 

45 

3.781596 

4.702358 

5.841176 

8.985008 

13.764611 

21.002461 

31.920449 

45 

46 

3.895044 

4.866941 

6.074823 

9.434258 

14.590487 

22.472634 

34.474085!  46 

47 

4.011895 

5.037284 

6.317816 

9.905971 

15.465917 

24.045718 

37.232012  47 

48 

4.132252 

5.213589 

6.570528 

10.401270 

16.393872 

25.728918 

40.210573  48 

49 

4.256219 

5.396065 

6.833349 

10.921333 

17.377504 

27.529943 

43.427419!  49 

50 

4.383906 

5.584927 

7.106683 

11.467400 

18.420154 

29.457039 

46.901613   50 

Pages  8,  9. 

3.  435,5589,14014. 

6.  556. 

7.  809. 

8.  566. 

9.  4805. 

10.  6454. 

11.  6458. 
13.  12225. 
i£  15772. 
16.  $8592. 

iX^es  10,11. 

18.  6928  votes,  less  ; 
8636  "   greater. 

19.  $149  ch.,  $201  w. 

20.  $181  B,  $319  A. 

21.  1917  less  no. ; 
2570  greater. 

22.  13,  875,  6716. 

23.  8. 

24.  4,  2. 

#5.  63  y.  V.  41  y.  P. 

26.  58  c.  47  a-b.  23  inf 

5  Off. 

27.  682  more. 

Art.  11.— 2.   1255440 

3.  1562292. 

4.  1441073. 

5.  1517644. 
7.  6950664. 
9,   4526818. 

10.  5212999. 

11.  6047136. 

12.  7956585. 
14.   67544325. 

rages  12, 13. 

16.  465507. 

17.  712236. 

18.  27600. 


19.  3458000. 

20.  17520000. 

21.  124704000. 

22.  495. 

23.  737. 

25.  62680257. 

26.  8435406375. 
29.   25038. 

SO.   57196. 

31.  253377. 

32.  323352. 
55.  5456256. 
36.   860209340. 
87.   9067243052. 
38.   5153209664. 

Pages  14,  15. 

41.  1873784. 

42.  2232321. 

43.  33104944. 

44.  40858938. 

48.  4698. 

49.  21760. 

50.  182975. 

51.  2015898. 

Page  17. 

3.  9626^. 

4.  7707*. 

5.  1792. 

5.  1312AV 

7.  46364. 

5.  2580|14|. 

11.  1104&- 

lift  9042^. 

15.  8325TV 

l£  13400*. 

Prices  19,  20. 

3.  2,  11,  13. 


4.  3,41,397. 

5.  2,  2,  3,  5,  41. 

6.  2,  5,  281. 

7.  3,  5,  5,  43. 

8.  2,  2,  2,  2,  2,  2,  2,  2, 

3,  5. 
5.  2,  2,  643. 
JO.  2,  2,  3,  3,  3,  83. 

12.  2. 

13.  2,  2,  3. 

14.  2,  2,  2,  3. 

15.  5,  5. 

JY/f/es  21-25. 

2.  m- 

Q      1503 

«*•    -'■SUT- 

4.  5TV 

/r     145 

O.     ^3T. 

0.  236^. 
7.  64. 

5.  $24. 

9.  36bbl. 

10.  676  bu. 

11.  38 §  reams. 

12.  6  men. 

^Lr*.  39.-2.  144. 

5.  2. 

£  46. 

5.  4. 

0.  19. 

7.  2. 

5.  16. 

£>.  2. 

10.  12. 

Xg.  4  Acres. 

13.  3  ft. 
X*.  14  ft. 
15.  16  yd. 

^•*.  45.-2.  210. 

3.  100800. 

4.  21168. 


Answers. 


319 


5.  3360. 

6.  9900. 

7.  51408. 

8.  34650. 

9.  1791700. 

10.  1388016. 

11.  2520. 
W.  5040. 
74.  30. 
15.  12  in. 

i0.  360  peaches. 

17.  180  weeks. 

18.  2f. 

25.  $31.68  ; 

72  H.,  9&  A.,  88  G. 

.Prtflres  45-50. 

4.  2540.42  m. 

J.  385  00024  Hm. 

6.  17232  m. 

7.  8960.008  m. 

8.  40157.575  m. 

9.  370.678307  Km. 

15.  836.0524  m.; 
83.60524  Dm. 

16.  75.842  m.; 
7584.2  cm. 

17.  18.762  m.; 
1876.2  cm. 

18.  6175000  cm.; 
61750000  mm. 

19.  1.58364  Hm. 

20.  285300  dm. 

21.  153000  Dm.; 
153000000  cm. 

22.  8634  ca.; 
.8634  Ha. 

23.  75000000  sq.  mm.; 
7500  sq.  dm. 

24.  82.34  A. 

25.  1.8438  Ha. 

28.  256034.089  cu.  cm. 

29.  38.450  cu.  m. 
SO.   253000000000  cu. 

mm. ; 
253000000  cu.  cm. 

31.  1.28653  dl. 
12.8653  cl. 

32.  3500  cl.; 

35000  ml.;  3.5  dl. 

33.  8000  liters. 

34.  800  DL;  80  HI. 

35.  238.47  dg.; 
2384.7  eg.; 


2.3847  Dg.; 
23847  mg. 

36.  0.025384  dg.; 
0.0025384  g. 

37.  2158  g. ;  215800  eg. 

38.  0.001  Kg. 

39.  31000600  g. 

Pages  51,  52. 

4.  70.925  bu. 

5.  19.295  gal. 

6.  223.704  mi. 

7.  .3047328  oz. 
9.  199.53325  A. 

10.  8829  cu.  ft. 

12.  2286  cm. 

13.  10972.5  g. 

14.  2609.7  cl. 

15.  3412.28  A. 

16.  .4046+  Ha. 

17.  60.746+  Ha. 

18.  1772.04+  lb. 

19.  995.334+  p. 
2.  10798.22  m. 

4.  93  cm. 

5.  0.3872  Km. 

6.  $362. 16829. 

7.  99.053  g. 

S.  25.028+  m. 
9.  $323. 

10.  1.44  fr.;  33.84  fr.; 
$2.53. 

11.  $31.70  gain. 

12.  $38,245  gain. 

13.  9 1  sters  each ; 
7.20  fr. 

Pages  55,  56. 

2.  1535220  sec. 

3.  1296000  sec. 

4.  762036  in. 

5.  3872448  in. 

6.  1401264  grs. 

7.  328291b. 

8.  790294i  sq.  ft. 

9.  13200  ft. 

10.  $39600. 

11.  $380250. 

12.  41  far. 

13.  $2104.70|. 

Art.  151.— 16.  1111b 
6oz.  11  pwt.  14  gr 

17.  386  bu.  2  pk.  6  qt. 

18.  4  d.  10  hr.  50  min 

34  sec. 


19.  5847  c.  74  cu.  ft. 

20.  857  bbl.  8  gal.  3  qt. 

2gi. 

21.  658  A.  90  r.  204  yd. 

22.  5907  r.  4  qr.  12  sh. 

Pages  57,  58. 

23.  20  m.  7  ch.  2  r. 

24.  $60.61. 

25.  $1790.25. 

26.  20  A.  13  sq.  r. 

260|  sq.  ft. 

27.  $1874.04. 

30.  200  rods. 

31.  1  pk.  5  qt.  If  pt. 

32.  f  gill. 

33.  45  lb.  12.8  oz. 

34.  6  d.  6  hr.  46  min. 

48  sec. 

35.  6  oz.  17  pwt.  3*  gr. 

36.  9  oz.  15  pwt.  18  gr. 

37.  9  hr.  28  min.  4.8  sec. 
3S.  6  fur.   30  r.    2  yd. 

7.2  in. 

39.  5406lTV  sq,  ft. 

40.  64  cu.  quar.  in. 

Page  59. 

44.  .688+  lb. 

45.  £.733  +  . 

46.  .0004958+  m. 

47.  T^hi,  or  .00382  lb. 

48.  .05625  gal. 

49.  .0580357  wk. 

50.  .0131579  ton. 

51.  $638.53. 

52.  $59.25ff 

53.  .0625  d. 

54.  .2903. 

55.  .4187. 

56.  .3808. 

57.  .03062. 

58.  .625. 

Pages  60,  61. 

2.  241  A.  1  sq.  r. 

3.  168  bu.  2  qt. 

4.  38  mi.  5  fur.  39  r. 

2£  ft. 

6.  2s.  lOd.  3  far. 

7.  8  oz.  13  pwt.  6  gr. 

8.  3  quarts. 

9.  4  d.  21  hr.  33  min. 


320 


Answers. 


10.  13s.  3d. 

12.  9  mi.  1  fur.  18  r.  7  ft 

10  in. 

13.  1  oz.  2  pwt.  6  gr. 
U.  £1  14s.  9d. 

15.  j. 

17.  6  yr.  6  mo.  5  d. 

18.  12  yr.  9  mo.  19  d. 

19.  46  yr.  1  mo.  17  d. 

21.  484  days. 

22.  109  days. 

Pages  62,  63. 

23.  462  days. 

24.  436  days. 

25.  374  days. 

26.  37  days. 

27.  1°  19'  14". 

28.  79°  8'. 

29.  62°  50'  30". 

Art.  158. 

2.  £74  lis. 

3.  143  gal.  2  qt. 

4.  580  m.  7  fur. 

5.  2  d.  20  hr.  5£  m. 

5  sec. 

6.  1355°  47'  56". 

7.  385  bu.  2  pk.  1  qt. 

8.  £37  9s.  lOd.  2  far. 
10.  2  gal.  2  qt.  2|  gi. 
ii.  3  bu.  2  pk.  1  qt.  f  pt. 
10.  3s.  7d.  3|  far. 

13.  5°  33'  16|". 
U.  91|  C. 

15.  9s.  2d.  2  far. 

16.  7772Tf3fr. 

17.  36|  doz. 
IS.  113i  mi. 
19.  7.182  Km. 

Pages  64,  65. 

2.  101°  22'. 
3   4°  48'. 

4.  13°  37'  42". 

5.  74°  1'  2". 

7.  3  hr.  13  min.  40  sec. 

8.  3  hr.  14  mi.  47|  sec. 

9.  10  o'clk.  7  m.  35f  s. 

10.  5  o'clk.  52  m.  26^  s. 

11.  1  hr.  15  min.  56  sec. 

12.  3hr.  31m.  46  s.; 
1  hr.  16  m.  47  s. 

13.  1  hr.  6  m.  17  sec. 


^Pages  67-69. 

2.  $101061. 

4.  580|  ft. 

5.  50  r.  wide  ; 
$351  T9e,  cost. 

6.  9f\  rolls. 

7.  $30804. 51  f. 

8.  194400  sq.  in. 

10.  80  rods. 

11.  46010|  sq.  ft. 

12.  17|  rods. 

13.  $367.00125 
Art.  178. 

15.  338  sq.  in. 

16.  29  A.  85  sq.  rods. 

Pages  70,  71. 

2.  $94,815. 

3.  262.144  cu.  m. 

4.  237^  loads. 

5.  169  U  cu.  ft. 

8.  3456  gal. 

9.  $10.93i 

10.  303.1875  ft. 

11.  $227.81^. 

12.  7.95  ft. 


Bages  72,  73. 

3.  21  ft. 

4.  16  4  ft. 

5.  $77.34|. 

6.  $7.48H- 

7.  585  cu.  ft. 

8.  5Hf|  cu.  ft. 

9.  $12.60. 
/0.  $318.93f. 

11.  243  boards. 

12.  2270|  ft. 

Art.  190. 

1.  73ff  perch. 


3.  197208  bricks. 

4.  $1493.85. 

Pages  74=,  75. 

2.  $1794.98. 

3.  $1258250. 
4-  $1.12. 

5.  $4,477  +  . 

6.  $3750. 

7.  13^  lots;  $6462 g. 
9.  $334,331 


10.  $450. 

11.  $842|. 

12.  $14.16f. 

13.  $66. 

14.  $98.50. 
15 r  $151.20. 

16.  $34,375. 

17.  $210. 

15.  $799.50. 

19.  $70420. 

20.  $2640. 
£*.  105  lbs. 
23.   $163, 
«&  $2164. 

Pages  76,  77. 

25.  $2.80. 

26.  22  planks. 
07.  13^  bales. 

29.  $57860. 

30.  $120. 

31.  $895H. 

34.  $4696.30. 

35.  $3914.625. 

36.  $1457.33|. 

38.  $12020. 

39.  $0,112  per  lb. 

41.  $26.0658. 

42.  $192.92. 

Ptoses  78-81. 


$163,745. 

$653.35. 

$152.98. 

$977. 

$241.27. 

$1588.75. 


Pages  83,  84. 

20.  .42,  or  42%. 

21.  .53f,  or53|%. 

22.  .46|,  or46|%. 

23.  .2l|,  or21f%. 

24.  .34ff,or34ff%. 

25.  .27^,  or  27&%. 

26.  .50,  or  50%. 
07.  .23f,  or23f%. 
30.  471. 

3i.  586.25. 
$£.  469.84. 

33.  313.38. 

34.  814.20. 

35.  7397.25. 
30.  6842. 


Answers. 


321 


37.  6.03£. 

38.  49.92  sq.  r. 

39.  $24.25  dif. 

40.  26.999  miles. 

43.  4f%. 

u-  m%- 

45.  5%. 
.46.  6^23%. 

47.  m%. 

4S.  18|f%. 

Pr/</e  85. 

49.  A°t%- 

si.  mi%- 

52.  10^%. 
5,?.  3f%. 

55.  16%. 

56.  \\%. 

57.  89ff%. 
55.  39T3T%. 
55.  77f%. 

eo.  8if%. 

61.  61£%. 

64.  4083J. 

65.  12480. 

66.  13814f. 

67.  2589. 

68.  139536. 

69.;  ioooooo. 

70.  $546. 

71.  £49660. 

72.  125300. 

73.  500000. 

74.  360TV 

75.  64.25. 

Page  86. 

76.  $555f. 

77.  $21000. 


79.  $85.93|. 

52.  21448. 

83.  1400. 

54.  2760. 

85.  4000. 

56.  5250. 

57.  3240. 
88.  600. 
59.  7000. 


90.   $9600  cost; 

$5^  perbbl. 
92.  $32000  cost; 

$15  per  bbl. 
92.   $7366  rV 

Page  87. 

1.  12432if- 

2.  .59ff|. 

3.  $69FVTloss- 

4.  17H  g.  per  ct. 

5.  $27368.42TV 

6.  180. 

7.  581.25. 

5.  15.12. 

9.  26.95  mi. 

10.  $24.25. 

27.  87f|56  gaiD. 

12.  $0.76*\. 

75.  .78f|  profit  %. 

14.  $30,998+  per  A. 

75.  18f%. 

76.  2516. 

77.  12%. 

Pages  90,  91. 

2.  $380.19. 

3.  $676,962. 

4.  $184.8413. 

6.  .3775,  or37f%. 

7.  $7.8125. 

5.  25%. 
9.  50%. 

79.  $627. 

12.  S2.35T3T. 

75.  $279£. 

14.  $1210.52i|. 

75.  .25. 

Pages  92,  93. 

2.  $27.343|. 

3.  $2707.50. 

4.  $2713.225 

5.  $15000  sale; 
$14625  owner  re'd. 

6.  $21.0732  com. 
$842.93  amt.  pur. 

7.  $621.30. 

5.  $16743  amt.  sale. 

9.  $26250. 
79.  $10000. 
77.  $24477.684  invest. 

$887,316  com. 
12.  $1172.25  com. 
75.  $5489.53. 


U. 
15. 
10. 
17. 
IS. 
19. 


937.172. 

$603.75. 

$363.48. 

$2920. 

$11006|. 

$425  com. 

$4575  pd. 


21.  $8196.583. 

22.  $292,875. 

23.  $12676.92. 

24.  $1733. 

25.  \\%. 

26.  $64,924  com.; 
$3181.276  spent. 

27.  $6819.43. 

28.  31363.63i7T  lbs. 

Pages  95,  96. 

2.  $33.50. 

3.  $30  gain. 

4.  $62,002  +  . 

6.  .008. 

7.  6|%. 

5.  .008i. 
79.  $169331-. 
77.  $4960. 

12.  $9090.90  +  . 

75.  $20872.72T8T. 

75.  $271683.67  +  . 

76.  $4329.897. 

77.  $26056.70 
75.  $14234.82  +  . 

Page  97. 

1.  $4£  per  $1000. 

2.  $5¥5T  per  $1000. 
5.  $487.50. 

4.  $15600. 

5.  $85478.47. 

6.  $314.50. 

7.  $12873.56. 
5.  $312.50. 
9.  $14.70. 

Pages  99-102. 

2.  100%. 
5.  39^%.; 

$983.6941  F. ; 

1573.91^  M.; 

786.95if  P.; 

1180.43HH. 

4.  20%  = 

5.  $555. 


322 


Answers. 


6.  $70312.50. 

Art.  267. 

3.  $51. 

4.  $232. 

5.  $77.20. 

6.  $548,375. 

7.  $302.93. 

8.  $496.13f. 

10.  $13193.717  +  . 

Pages  104,  105. 

3.  $87.32. 

4.  $805.49. 
5. '$902. 79. 

6.  $669. 

7.  $1138.66|. 

8.  $22.77. 

5.  $26.46. 

10.  $145.91  +  . 

11.  $144,375  int. ; 
$2644.375  amt. 

rages  106,  107. 

13.  $179.62. 
H.  $17.55. 

15.  $626.40. 

16.  $4474.96|. 

17.  $103,039. 

18.  $2096.1243. 

19.  $65,875. 

20.  $104,498. 

21.  $104,796. 
$60,144. 
$163,457. 
$119,574. 
$2213.76. 
$7944.62. 
$1234.67. 
$988.38. 


22. 


25 


30.  $1059.26. 

31.  $625,567. 

32.  $355.30; 

Nov.  24th.  1887. 

Pages  108,  109. 

2.  $707.53. 

3.  $40.79. 

4.  $149.34. 

5.  $2869.93. 

6.  $4623.06. 

7.  $101. 

8.  $50.98. 


9.  $425.65. 

10.  $134.72. 

11.  $68.04. 

12.  $195.16. 

13.  $1024.25. 
U.  $664.32. 
15.  $1296.875. 

Art.  284. 

2.  $8,925. 


3. 

4- 
5. 
6. 
7. 
8. 
9. 
10. 

11. 

H. 

15. 

10. 
17. 
IS. 
10. 
20. 
21. 


$5.20. 

$4.73. 

$7,686. 

$677,259. 

$791,868. 

$1211.33i. 

$2551.66  +  , 

$400,318. 

$637.88. 

$31.25. 

$6.00. 

$100,048. 

$35,445. 


$40.63. 
$26.19. 
$251.81. 


Pages  110,  111. 

24.  $8.40. 

25.  $146.78. 

26.  $1329.57. 

27.  $16.90. 

28.  $60.04. 

29.  $61.04. 

Art.  288. 

2.  $130,985. 

3.  $121.32. 

4.  $104.95. 

5.  $360,412. 

6.  $316,898. 

7.  $162.08. 

8.  $9.69  at  4%  ; 
$12.11  at  5%  ; 
$16.95  at  7%. 

9.  $17.30  at  4%  ; 
$21,576  at  5%  ; 
$30,206  at  7%. 

10.  $30.30  at  4%  ; 
$37.88  at  5%; 
$53.03  at  1%. 

11.  33.66  at  4%; 
42.09  at  5%  ; 
$58.91  at  7%. 


12.  $63.05  at  4%  ; 

$78.77  at  5%  ; 
$110.27  at  7%. 

13.  $170.48  at  4%; 
$213.08  at  5%  ; 
$298.31  at  7  %. 


Pages  112.  113 

2. 

$3080. 

3. 

$3083.46^. 

4. 

$16126.20. 

5. 

$17902.50. 

6. 

$18425.625. 

Art.  292. 

•2. 

8%. 

3. 

6%. 

//• 

lrh%. 

5. 

6%. 

(J. 

6%. 

7. 
8. 

7%. 

9. 

5%. 

10. 

10.3+%. 

Pages  114,  115. 


12. 

13.  $58333i. 

14.  $55555 1. 

15.  $360. 

17.  $535.71?. 

18.  $1264.41  + 

Pages  115,  116. 

19.  $179.25. 

20.  $220. 

21.  $3456.54. 

22.  $375.60. 

24.  .5  yr.,  or  6  mo. 

25.  2.055+  yr., 

or  2  yr.  20  d. 

26.  16|yr.,orl6yr.8m. 

27.  1.399+  yr., 

or  1  yr.  4  m.  23  d. 

28.  1.069 +  , 

or  1  yr.  25  d. 

30.  8^  yr.,  or  8  yr.  4  m. 

31.  9.52A,  or  9  yr.  6  m. 

9  a. 

82.  28  years. 
Pages  118, 119. 

2.  $498,962. 
8.  $498.59. 


Answers. 


323 


4.  $4149.68. 

6.  $252,233. 

7.  $2633.51. 

Pages  123,  124. 

12.  £5  2s.  Id.  34  far. 

13.  £10  18s.  3d. 

14.  £111  13s.  4d. 

2.  $328.78. 

3.  $2090.098. 

4.  $3390.048. 

Pages  126,  127. 

6.  $4466.987. 

7.  $3040.4565. 

8.  $819.65+. 

9.  $7622.336. 

10.  $2981.21. 

11.  $2149,294. 

12.  $1900.155. 

13.  $3787.218  +  . 

14.  $1200. 

15.  $1115.398  +  . 

16.  $100. 

rages  127, 128. 

2.  $871,789,  p.  w. ; 
$78,461,  tr.  d. 

3.  $2827.21  +  ,  p.  w.  ; 
$445.29,  tr.  d. 

4.  $5995.652,  p.  w.  ; 
$899,348,  tr.  d. 

5.  $7473.65,  p.  w. ; 
$1177.10,  tr.  d. 

6.  $8661,  p.  w. ; 
$1339,  tr.  d. 

7.  $177,455,  Dif. 

8.  $2500. 

9.  $805.66  better,  cash, 

Pages  129,  130. 

2.  $836,825. 

3.  $875.70|. 

4.  Sept.  2d,  maturity  ; 
12  d.,  term  of  dis. ; 
$5287.11,  Pro.     ' 

5.  $3.24,  Dif. 

6.  $859.69. 

8.  $933.20. 

9.  $8527.16. 
10.  $5545.95  +  . 

Art.  317. 

3.  $5073.17  +  . 

4.  $8375.63  +  . 


5.  $3307.888  +  . 

6.  $2807.88  +  . 

rages  133-136. 

1.  $5,425,  B.  dis.  ; 
$344.58,  Pro. 

2.  $5.25,  B.  dis.  ; 
$494.75,  Pro. 

3.  $1217.86|. 

4.  $1215.63^  at  7%  ; 
S1211.16§  at  5%. 

5.  $426.71  +  . 

6.  $709.33^. 

7.  $712.25. 

8.  $1616. 

9.  $520,  1st  Amt.  ; 
$515,  2d  " 
$510,  3d  " 
$505,  4th  " 

10.   $523,331,  1st  Amt. 
$517.50,  2d  " 
$511.66|,  3d  " 
$505. 83J,  4th  " 
At5%,$516.66f,lst. 

$512.50,  2d. 

$508.33^  3d. 

$504.16|,4th. 

14.  $471,596. 

15.  Apr.  4,  1883,  mat.; 
$9,304,  Dis.  ; 
$1153.696,  Pro. 

16.  Mat.,  July  44th; 
$25,  Dis.  ; 
$2475,  Pro. 

Pages  139-142. 

3.  1.84+  mo.,  or55d. 

4.  5  m.  23  d. 

7.  Jan.  29th. 

8.  Sept.  1,  1879. 

9.  4  months. 

10.  62davs. 

11.  Aug.  10 

12.  32  d.,  or  to  Aug.  2 

Pages  143-146. 

14.  67  days. 

15.  8  days. 

17.  $910,  Bal.; 
Due  Apr.  28. 

18.  $945,  Bal.  ; 
Due  July  7th. 

19.  $510,  Bal. ; 

Dec.  30,  Av.  time. 


Pages  147-149. 

20.  $906.54,  Bal.  ; 
Due  June  10th. 

21.  $100,  Bal.  ; 

P'bl.  Nov.  14,  1883. 

23.  $290,  Bal.  ; 
Due  Aug.  5th. 

24.  $435,  Bal.  ; 
Due  July  12th. 

25.  $1780,  Cr.  Bal.  ; 
Due  Mar.  17th. 

26.  $140,  Bal.  ; 

Due  Dec.  20th,  1879. 

27.  $100,  Cr.  Bal.  ; 
Av.  date  June  17th. 

28.  $1190,  Bal. ; 

Due  Aug.  14th,  1883. 

Pages  152-154. 

31.  $121.62,  Cash  Bal. 

32.  $670.82,  Cash  Bal. 

33.  $677,105,  at  8#. 

34.  $221.33.  Cash  Bal. 

35.  $1229.90,  Cash  Bal. 

36.  $1462.07,  Cash  Bal. 

37.  $199.52,  Cash  Bal. 

38.  $199.52,  Cash  Bal. 

39.  $201.45,  Cash  Bal. 

40.  $1903.81,  Cash  Bal. 

Pages  155-157. 

2.  $15234.12,  Net  pro. 

3.  $12002.45,  Net  pro. 

Art.  366. 

5.  $14161.44,  Net  pro.; 
Due  Jan.  8th. 

6.  $3484.43,  Net  pro. ; 
Due  Nov.  23d. 


Pages  161-163. 

Art.  382. 

2.  $400.60ff,A's  share; 
$549.39f|,  B's     " 

3.  $374.46ff ,  A  ; 
$425.53TV  B. 

4.  £5517.24^,  A; 
$3972.41^,  B  ; 
$3310.34^,  C. 


324 


Answers. 


5.  $10000,  Net  cap. 

close  ; 
$6C36f,  A's  floss; 
$3333|,  B'gi     " 

6.  $3461^,  X's  share  ; 
$2307 ^  Y's     " 
$173011,  Zs      " 

7.  $1500,  A's  share ; 
$1800,  B's      " 
$750,  C's 
$4500,  D's      " 

8.  $1800,  share  of  1st  ; 
$1200,  "  2d  ; 
$900,         u        3d. 

9.  $180,  B's  share. 

10.  $3125,  sh.  of  1st  ; 
$9375,      "      2d. 

11.  $13554,  A'sdiv.; 
$9036,  B's      " 

14.  $347||,  A's  gain  ; 
$278  4,  B's      " 
$173|i  C's     " 
$4347^1,  A's  net  cap. 
$3478^3,  B's     " 
$2173|i,  C's      M 

15.  $4933^,  A's  net  cap.: 
$2366-1,  B's      " 
42f%  loss. 

rages  166,  167. 

19.  $14207.50,  Firm's 
net  g. ; 
$17768.25,  C's  net 

cap. ; 
$15691.75,  D's  net 
cap. 
£1.  $9266.68,  A's  cr.  bal 
$8963.93,  B's     " 

23.  $419.41^,  A's  sh. ; 
$528.15^,  B's    " 
$652.42T7o4s,  C's    " 

24.  $878.04ff ,  A's  sh. ; 
$526.82ff ,  B's  " 
$395.12¥8T,  C's  " 

Pages  168,  169. 

26.  $19541,  A's  profits  ; 

;*,  B's    " 


27.  $1411^,  share  of  X; 
$1411|f,  "  Y; 
$1176^,       "       Z. 

28.  $35.00,  A's  part ; 
$30.00,  B's    " 
$22.50,  C's    " 

29.  $1875,  A's  share ; 
$10412,  B's  " 
$20831,  c's  " 

30.  $3510,  A's  part ; 
$2730,  B's  « 

31.  $9721  fj -§,  A's  part; 
$12344* |f,  B's  " 
$9133f  $-?-,  C's  " 

32.  $7784 ,85,  A's  part; 
$7851f|,  B's  " 

33.  $25454T6T,  A's  part; 
$40000,  B's 
$54545-^,  C's  " 

Bages  170,171. 

2.  $1854.02^1,  A's 
part; 
$1312.08Tf  F,  B's 

part ; 
$1083.89^,  D's 

part ; 
28T7T87  per  cent. 
8.  $2171  ;  26+  %. 
4.  $7907.70,  A's  part ; 
$8933.25,  B's    " 
$9391.20,  C's    " 
64|  per  cent. 

Art.  393. 

1.  $1650,  A's  loss  ; 
$1100,  B's    " 
$550,  C's      " 

2.  13i£  per  cent. ; 
$2142.85|,  A's  loss. 

3.  $1307.14|,  Ins.  Co. 

real  loss. 

4.  19^fT%  loss; 
$510.34#3,  Co.  B's 

real  loss  ; 
$2063.92ML  Co.  C's 

real  loss  ; 
$43.77|f  i ,  Co.  D's 

real  loss  ; 
$4002.85o4/3,  Co.  A's 

real  loss  ; 
$5502.85^3, 

vessel's  real  loss. 


Pages  173-177. 

2.  $794,  carriage  ; 
$1062,  horses. 

3.  5586. 


7.  £227  12s  Id. 

8.  f . 

11.  4605  sheep. 

12.  66  years. 

13.  1440. 

15.  $41,205. 

16.  $3536.25. 

17.  $14760. 

19.  $6937.60,  sold ; 
$1737.60,  profit. 

20.  $85.80. 

21.  72%. 

22.  3600. 

23.  $4104. 

25.  $430.36  +  . 

26.  $1265.06+. 

28.  $27.30. 

29.  9%. 

30.  9%. 

31.  10+%. 

32.  2  years. 
S3.  3  yr.  4  mo. 
34.  $1388.88$. 
85.  $4390.24^- 

36.  $1010.61  r8&V 

37.  $3309.84+. 

38.  $1791.66|. 

39.  $6474. 66|. 

40.  $54.38. 

41.  $325,  A  ;  $175,  B  ; 

$100,  C. 

42.  339T  hours. 

44.  $203. 

45.  250  shares. 

46.  $85. 

47.  14046  523  times. 

48.  22|%. 

49.  16  yr.  8  mo. 

50.  $12380r^. 

51.  $124.96. 

52.  $640,  A's  share  ; 
$840,  B's      " 
$840,  C's      " 

53.  $350. 

54.  7  o'clock  51  m.  12  s. 

55.  3750=';  2500  =  i; 
1250  =  I. 


Answers. 


325 


56.  19i%;$1933.33i  A 
$725,  B ; 
$2390.08*,  C 

57.  i  hr.,  or  15  min. 

58.  $960,  A:  $1440,  B; 
$2160,  C. 

59.  244.  mo.,  or  in  3  mo. 

60.  s4:02  +  . 

61.  $116.28  +  . 

62.  $30666§. 

63.  $15.29. 

64.  6£%. 

65.  2807?|  cords. 

66.  $12000. 

JPages  183,  184. 
Art.  430. 

4.  80A  mo. 

5.  128  spoons. 

6.  3584J  Km. 

7.  lj  yd.  wide. 

8.  $359,892  +  . 

9.  $10.50. 
$74. 
$4830. 
12£  tons. 


10. 
11. 
12. 
13. 


Panes  186,  187. 

3.  42davs. 

4.  5004  bu. 

5.  160  ft, 

6.  $674. 

7.  154  min. 

8.  720  pair. 

9.  Ill  lb. 

10.  $15,774. 

11.  32  pp.  ' 
i&  2|  days. 
2.?.  18  coin. 

14.  .36. 

15.  2  days. 
26.  15  ft. 
17.  2£  ft. 

-4r£.  431. 

2.  244,  1st ;  192,  2d  ; 
288,  3d. 

Page  188. 

S.  200,  A's  shares ; 
100,  B's      " 
150,  Cs      " 


4.  $2200,  A's  share  ; 
$2933i,B's    " 
$3666f,  C's    » 

5.  $4150,  A'sinvestm 
$4950,  B's 
$5150,  C's 
$4250,  D's 

7.  84  fc  1st  part ; 
169, 2d      " 
190,  3d      " 
138i,  4th  " 

8.  $189  ft,  B's  money 
*379-ft,  C's      " 
$75f\,  A's 

9.  $79.20. 

10.  $7.20. 

11.  $71 6f,  A's  share; 
$895  5-,  B's      " 
$5374,  C's       " 

12.  $450;  A's  money; 
$800,  B's 

13.  $3363^  =  1st  ; 
$5045T5T  =  2d ; 
$10090}?  =  3d. 

Pages  190,  191. 

3.  $8642.725. 

4.  $6853.55|. 

5.  $9936.71f. 

6.  $7512.30. 

7.  $4845. 

8.  $12367.50. 

9.  $4208.  134. 

10.  $843625. 

11.  $4381.50. 

12.  $1140.50. 

13.  $8408.964,. 

14.  $9641. 93|. 

16.  $6293.1925. 

17.  $4430.25. 

15.  $5684. 

19.   $9857.793f. 

Pages  195,  196. 

2.  $8484.937^. 

3.  $17177.60. 

4.  $73570.96875. 

5.  $13583.819+  ; 
$13513.799  +  . 

6.  $17092.38; 
$17421.764+  ; 
$17217012. 

8.  £3134  lis.  7d. 

9.  £5187  5s.  6d. 


10.  £1741  16s. 

11.  $4.80. 

12.  $3.7534  +  . 

t  13.  £11  15s.  6d.,  or 
$52,565. 

14.  $4.91. 

15.  £3832  18s.  5.7d. 

16.  £2036  7s.-4.8d.; 
At  $2.97  per  yd. 

Pages  197,  198. 

18.  $112.31,  dif. 

20.  23535  f  r. 

21.  §230.769. 

22.  $150.32,  dif. 

23.  $391.95. 
25.  $916.75. 

.  7856.08,  M. 
29.  7399.472,  M. 
SO.  11946f,  M. 

32.  $1645. 

33.  $3561.45  +  . 

34.  .63. 

35.  $532,072. 

36.  $626,163. 

Pages  201,  202+ 

2.  $123.75. 

3.  $2190.61  +  . 

4.  $10645.937  +  . 

5.  $2175.331,  duty ; 
$8090.562,  cost. 

6.  $1920.10|. 

7.  $660,832. 

8.  $5583.0074. 

9.  $994.31. 

10.  $903.60  +  . 

11.  $4278.237  +  . 

12.  $1043.86  +  . 

13.  $584.26. 

14.  $607.95,  duty  ; 
$6960.064,  cost. 

15.  $4950.  duty; 
$10363.36,  Bill ; 
$15313.36,  D.  &  cost. 

Pages  208 ,  209. 

1.  $450000000,  Issue ; 
$22500,  Fund. 

2.  -S33650,  proceeds ; 
300  shares. 

3.  $4627.30,  tax. 

4.  $180000,  B.  notes. 


326 


Answers. 


5.  $2936.925,  A; 
$3788.07f,  B ; 
$2053.29  +  ,  C. 

Art.  489. 

2.  $351.65,  Bal. 

Pages  213-215. 

5.  $412.40,  Bal. 

6.  $201.54,  Bal. 

7.  $259.6H,  Bal. 

8.  $747,561,  Bal. 

9.  $298.00,  Bal. 
10.  $683.12|,  Bal. 

Bages  224=,  225. 

tf.  $100100. 
4.   $5070. 

6.  $8165.625. 

7.  $111T%5T  per  share. 

8.  $968.87£. 

10.  $4375. 

11.  $38200. 

13.  9f%. 

14.  3|%. 

16.  160  shares. 

rages  226,  227. 

27.  13  2  3  certs,  of  1000 
bbl. 

18.  714£ff  shares. 

19.  400  shares. 

21.  $50  per  share. 

22.  $266|  per  share. 

24.  $108281^. 

25.  $33187.50. 

26.  $35840. 

27.  $35416|. 

28.  $63600. 
81.  .03861TV 

*J~.     .UOff6?. 

.&?.  4  per  cent.  @  122f  ; 
$28.83,  better. 

34.  $65.25,  diff. 

35.  $450,  rec'd; 
4%  on  cost. 

Pages  228,  229. 

37.  17TV%. 
39.  3ft  %. 


44.  $96¥8T  per  share. 

45.  $109f  per  share. 

46.  $438|f, 

or  $87ff  per  s. 

Art.  559. 

1.  $66f. 

2.  $100  per  share. 

Pages  230,  231. 

3.  20-yr.  bond  @  90. 

4.  A,  100%; 

B,  50%  ; 

C,  40%  ; 

A,  1000000 ; 

B,  750000  ; 

C,  250000 ; 
l-i9^  shares. 

5.  $26933i 

6.  $32.41. 

7.  7tVt%- 


10.  $300. 

11.  Chem.  Bank  ; 
$107.14f,  better. 

13.  $312.50,  gain. 

14.  86f  acres. 

15.  $3325. 

16.  .07f£. 

17.  $3750. 
25.15^%; 

12|f%. 

19.  R  R.  Stock ; 
.00f,  better. 

20.  $150. 

21.  $7560. 

22.  7|%. 

JVtflres  £32,  233. 

05.  33i%  dis. 
&£.  $187*. 

25.  $196.02. 

26.  $625.00. 

27.  8tf  %. 
0£.  $11200  ; 

50  sh.  each. 
00.  $5205. 
30.  2C0  shares, 
or  $20000. 

Art.  561 

1.  8ff%. 


2.  $551,994. 

3.  $1506.18. 

4.  $1.23  per  bu\ 

5.  481.59  tons. 

Pages  234,  235. 

6.  634  notes. 

7.  lift?',  22+%. 

8.  4%  com. 
5.  $600. 

10.  To  pay  cash  ; 
$742.50  better. 

Art.  565. 

2.  $979.65. 

3.  $19.41f. 

Pages  239,  240. 

2.  $266.10. 

3.  $13236. 

4.  $64378.07+  C.  int.; 
$29835  f .  rec. 

5.  $621.36. 

6.  $880.64. 

7.  $1612.80  less. 

8.  $2.20. 

9.  $14633.40; 
$47697.75,  End'w't. 

10.  $805.92. 

11.  $7544  less. 

12.  $11617.20. 

13.  $20817,  Bank; 
$2817  more. 

14.  $1289.05  less ; 

Pages  242-247. 


4.  $3924.32  +  . 

Art.  597. 

3.  $1001.179  +  . 

4.  $13417.085  +  . 

6.  $4692.537. 

7.  $3366.37  +  . 

8.  $44632.425. 

10.  $4212.93  +  . 

11.  $8142.008,  at  21  ; 
$5847.622,  P.  w. 

13.  $50000. 

14.  $11199.303  +  . 

15.  $43219.424. 

Pages  248-250. 

2.  $2660.974  +  . 

3.  $23739.647  +  . 


Anstvers. 


327 


4.   $15622622442. 

6.  36  yr.,  and  a  bal.  of 

£33309296. 

7.  42  yr.,  and  a  bal.  of 

$33667195. 

8.  5  yr.,  and  a  bal.  of 

$2311236.22  +  . 

10.  $191005.524. 

Art.  605. 

11.  $27173.596  +  . 

12.  $43477.76. 

13.  $296048.80. 
U.  $5174.10. 

Pages  254,  255. 

0.  54. 

3.  729. 

4.  16.96  +  . 

5.  .28. 

6.  .87576  +  . 

7.  32.7679  +  . 

8.  .0976  +  . 

9.  785.64. 
10.  60.7042  +  . 

Art.  622. 

13.  tf. 

U.  ft. 

15.  ff. 

16.  ft. 

18.  59TV+  rods. 

29.  42.426  +  r.  side. ; 

11.25  A. 

20.  176. 

02.  1838.265625. 

22.  20  ft. 

05.  11.3137+  in. 

24.  58.864+  ft. 

25.  17.889  rods. 

26.  84  ft.  wide. 

Pages  257,  258. 

2.  34. 

3.  47  +  . 

4.  1.208 +  . 

5.  47.7  +  . 

6.  6.006 +  . 

7.  358.9  +  . 

8.  1.18 +  . 

9.  5.000006 +  . 

19.  345. 
12.  \. 
IS.  TV 


14. 


ft* 


26.  99.9  +  . 
17.  51.01  +  . 
25.  17.51+  in. 
29.  108.8+  in. 

20.  132.5+  in. 

21.  5903. 

22.  53.7+  in. 

23.  408. 
04.  763. 

P«</es  259,  260. 

3.  36  sq.  ft. 

4.  7£mi. 

5.  1121|  sq.  in. 

6.  34.6+  ft. 

9.  575000  cu.  ft. 

20.  15.64  ft. 

11.  4188.16  cu.  ft. 

12.  1429ilbs. 

13.  18|  in.  diam.,  8  in. 

deep. 

14.  19774^  Kg. 

15.  799.41b. 

16.  $3600. 

17.  79.54+  rods. 
25.  5.25  cm. 

Page  263. 

1.  800  sq.  ft. 

2.  $200. 

3.  $15.91^. 

4.  $90. 

5.  19800  sq.  ft. 

6.  2200  sq.  ft. 

7.  8  rods  wide  ; 
40  rods  long. 

8.  22500  bricks. 


10  breadths. 
99fiyds.; 

11  breadths. 


Pages  264, 265. 

1.  192  sq.  ft. 

0.  224  sq.  cm. 

3.  $7.92. 

5.  724.56+  A. 

6.  249.4+  sq.  ft. 

8.  10^  rods. 

9.  14  yd. 

10.  70|H  rods. 


20.  768  rods. 
25.  44  yd. 
2^.  138  ft.  11«  in. 
Z5.  56TfTrods. 

JPagres  266,  267. 

4.  113.318+  in. 

5.  71.52+  r.  per  sq.; 
63.39+  r.  per  circle; 
8.13+  rods,  dif. 

6.  30.27+  rods. 

7.  1590.435  sq.  ft. 

8.  57494  sq.  ft. 

9.  263.8944  feet. 

10.  23.888+  sq.  rods. 

11.  11309.76  sq.  r. 

20.  30  yd. 

13.  141.372  rods; 
376.992  rods. 

14.  203.717+  Acres. 

Art.  655. 

16.  200  sq.  in. 

17.  6.324+  in. 

18.  162  sq.  in. 

19.  58.5362  sq.  dm. 

Pagrs  26S,  269. 

21.  42.315  rods. 

00.  49.74  sq.  r.  cir. ; 
39.06  sq.  r.  square  ; 
10.68  sq.  r.  more  in  c. 

Art.  666. 

3.  412|  sq.ft. 

4.  3168  sq.  ft. 

5.  450  sq.  ft. 

6.  14.1372  sq.  ft.  con.  ; 
17.6715  sq.  ft. 

entire  s. 

Pages  270,  271. 

8.  47.124  cu.  ft. 

9.  59.0857+  gal. 

10.  18400  cu.  ft. 

11.  375  cu.  cm. 

20.  800  cu.  dm.,  or 

liters  ; 
0.8  Kl. 
13.  19614  cu.  in. 

15.  96  sq.  ft. 

16.  131.9472  sq.  ft. 

17.  418.3  sq.  ft. 

18.  3769.92  sq.  ft. 


328 


Answers. 


rages  272,  273. 

21.  5151.157^  lb. 

22.  9.163  ca.  ft. 

23.  333  cu.  ft. 

25.  $41,469  +  . 

26.  201062400  sq.  m. 

27.  31416  sq.  cm. 

29.  259777100108cu.ini 

30.  28.2744  cu.  dm. 

31.  2982  065625  cu.  ft. 

32.  3.541+  hhd. 

Pages  274,  275. 

2.  33.614+  gal. 

3.  1059.5286  liters. 

4.  658.125  gal. 

5.  102.9384  gal. 

6.  $3.95  per  gal. 

7.  3.31  bu. 

8.  8  in. 

Art.  684. 

2.  568r\tons. 

3.  241.164  bu. 

4.  57.024  bu. 

Pages  276,  277. 

5.  $49.13. 

7.  50  ft. 

8.  122|ft. 

Art.  687. 

2.  1152  sq.  ft. 

3.  294  sq.  ft. 

4.  72  sq.  ft. 

6.  13  boards. 

7.  9.4  bd.  18  ft.  long ; 
155H  bd.  ft. 

Art.  689. 

8.  22^  cu.  ft. 

9.  26~cu.  ft. 
10.  12.726  in. 

Pages  278,  279. 

1.  18756699. 

2.  16330115. 

3.  992385222. 

4.  11496. 

5.  $5.27. 

6.  714. 

7.  $3192. 

8.  315  eggs. 


9.  15680  men. 

10.  $31233±. 

11.  5  bu.  1  pk.  6\  qt. 

12.  77.14+  bu. 

13.  40791422655. 

14.  75. 

15.  12  =  g.  c.  a. 

16.  63|  smaller ; 
80£  larger. 

17.  1J§ ,  sum  ; 
ff,dif.; 

a  prod. ; 
l|f,  quot. 
IS.  5. 

19.  $440. 

20.  224.67^  bbl. 

21.  $33^.  '" 

22.  $3.40. 

£?.  94.54|  planks. 

24.  $450. 
55.  71  hr. 

26.  73.84+  ft, 
57.  38.416+  ft. 

25.  50%. 

29.  $3675. 

Pages  280,  281. 

30.  $31^,  A's  part  ; 
^o9^tj",  jj  s 
$78££,  C's    « 

31.  95f%. 

55.  2|  cts.  gain. 

33.  $104.65. 

34.  77  Ha. 

35.  $658.35. 
#?.  $72. 
37.  96  ft. 
55.  2280. 

39.  439^1 ,  sum  ; 
87ff,  dif.; 
46333TX5,  prod.; 

iftff .  qu(>t. 

40.  $12525. 

41.  $0.74i. 
4f.  60|§t%- 

4c?.  $12432.432  +  . 

44.  $6.73243728. 

45.  $3.83  ioss. 

#.  $5329.03  profit. 

47.  71  bu. 

45.  8.999+  bu. 

49.  967  cars. 


56).  $115.09  loss. 

51.  $19.89. 

55.  88%. 

J5.  242|  acres. 

54.  847170  Phil. 
1206299  N.  Y. 

55.  3364  Ca. 

56.  93±  sq.  ft. 

57.  363.73ift. 

Pages  282,  283. 

58.  $745,875. 

59.  3  shares. 

60.  28*%- 

61.  44.204  ft. 

62.  $12000. 

63.  .00^. 

65.  106.08  cu.  m. 

66.  $450.84. 

67.  540  bbls. 

68.  $2120.60. 

69.  $2760.69. 

70.  1019  in. 

71.  2.7  cm. 
;.?.  3  mo. 

73.  23,  r/.  c.  d. 

74.  $23809.52. 

75.  108  lbs. 

76.  $3.50  per  yd. 

77.  107,  r/.  c.  d. 

78.  $599.34. 

75.  113097.6  cu.  in. 

5#.  64.75,  Ha. 

81.  39.38  +  .  HI. 

82.  $271,845  +  . 

83.  6.3  in. 

84.  Wh%. 

85.  $11609.76. 

86.  $665.37. 

87.  $127.73. 

Pages  284,  285. 

88.  *$1 87.20. 
,89.  Oct.  16th. 

90.  Dec.  6th,  1883. 

91.  $1962.01. 

92.  44  ft. 

93.  8. 

94.  9. 

95.  6. 
95.  3375. 
97.  200%. 
9S.  $2470.75. 


Answers. 


329 


99.  178.731  bu. 

100.  49140. 

101.  18  ft.  wide ; 
54  ft.  long. 

'  102.  $595. 

103.  5.19  ft. 

104.  156  rods. 

105.  $3405.30,  Bank  ; 
$4905.30,  all. 

106.  7  + in.  =  1  side. 

107.  132.9+  meters. 

108.  1  yr.  1  mo.  14  d. 

109.  $2174.585  +  . 

110.  24dif. 

111.  1970.80  sq.  r. 

112.  $8.91  per  bbl. 

113.  126.589  Km. 

114.  78  mi.  211  r. 

5.332+  yd. 

115.  Ufa. 

Pages  286,  287* 

1.  75635. 

0.  586916. 

3.  754108. 

4.  6783002. 

5.  7388520. 

6.  1731704. 

7.  1010663. 
&  948395. 
9.  982110. 

10.  1183219. 

£2.  1199035. 

12.  725522. 

!«?.  661945. 

14.  549253. 

15.  1417691. 

16.  974687. 

17.  1162790. 

18.  379261. 

19.  1373105. 
£0.  1486901. 
01.  3193. 
22.  1856. 
05.  89111. 
24.  89189. 
05.  88909. 
00.  164808. 
07.  366185. 
05.  665645. 
29.  611111. 

50.  111109. 

51.  89111. 
*   50.  164898. 


55.  484737. 

84.  259331. 

55.  4436640650. 

36.  1817822786. 

37.  2626568694. 

38.  1331846875. 

39.  2023209268. 

40.  1398214650. 

41.  1777211634. 

42.  4130024886. 

43.  1431347492. 

44.  3468401325. 

45.  223702272. 

46.  1538746950. 

47.  768264600. 

48.  4405321875. 

49.  4084589512. 

51.  68851T3A9*V 

52.  51846T9TVVT- 

53.  2044181HH. 

54.  377582£ffff. 

55.  83132|ff|f. 

56.  30687ff{ft. 

57.  24368fffff- 

58.  9677¥V353<V- 

59.  22965||ff|. 

00.  107932if£f 

61.  9392ff|f. 

00.  122599^%, 

05.  17610HH- 

64.  82092Bfft. 

05.  15864S##r. 

Art.  692. 

1.  18A-0, 

2.  2dffr%.     • 
5.  $110.22. 

4.  $267,682. 

5.  33|%. 
0.  43f%. 

7.  14*%. 

8.  $2205.88TV 

9.  $1275. 

10.  1  yr.  3  m.  16  d. 

21.  $638.37  +  . 

12.  $96.47. 

25.  $58.62i. 

24.  6%. 

25.  .005. 

20.  $2743.33i 

17.  $30.94. 

25.  $85.01. 


29.  $54.60. 

00.  £40  17s.  2d.  2.56 

far. 

02.  $7020,  pro. ; 
$180,  com. 

22.  $51 

Pages  288,  289, 

23.  $448. 

24.  $2285. 

25.  $6000. 
00.  $1584. 

27.  $791896. 

28.  $135.30. 

29.  $118,625. 

30.  6£%. 

52.  $8251.67^. 

32.  3  yr.  4  m.  12  d. 

33.  $2392.34. 

34.  $2564.102  +  . 

35.  3  yr.  10  m.  6  d. 
50.  $3072. 

37.  6£%. 

38.  $60. 

39.  $16640. 

40.  Oct.  10th. 

41.  £1552  19s.  3.6d. 


#.  6TW%. 
45.  None. 
40.  9%. 
47.  .00f$. 

^r#.  6,95. 

1.  36897f  fr. 
0.  59.56  meters. 
5.  127  fields. 

4.  1323.2248  HI.; 
$7507.98.     . 

5.  3|  m.  c. 
0.  44  men. 

7.  22.7  cm. 

8.  0.557  m., 

or  5.57  dm. 

9.  7.503  dm. 

10.  3.9+  cm. 

11.  113.0976  cu.  dm. 

Pages  290,  291. 


3.  &. 

4.  A- 

5.'#. 


330 


Answers. 


6. 

jmr* 

7. 

^iff- 

S. 

*V 

9. 

tIt. 

1<>. 

tV 

11. 

51  bags  ; 

3f  bu.  in  each. 

12. 

332  lots;  T\5  A.  each 

Art.  697. 

2. 

24. 

3. 

*£  =  15f . 

4. 

isjA  -  402f. 

5. 

*-740  =  97!!, 

6. 

6f  davs  ;  A,  10  t. ; 

B,  15  t.;  C,8t. 

7. 

5  hr.  20  min. ; 

meet  at  stg.  pt. 

8. 

8  hr.  walk  ; 

22  times  No.  1 ; 

28  "  No.  2 ; 

33  "   No.  3. 

rages  293,  294. 

2. 

515944. 

3. 

45327848. 

4- 

53837066. 

5. 

675159828. 

7. 

2916  ;  3025  ;  3364. 

8. 

2704  ;  3136  ;  3481. 

10. 

2025  ;  4225 ;  7225 ; 

9025. 

12. 

11025  ;  13225  ; 

21025;  18225. 

u. 

59004. 

15. 

82852. 

10. 

29623. 

17. 

31394. 

Art.  709. 

5. 

June  3. 

G. 

320  y.  3  m.  8  dys. 

7. 

Friday,  May  16. 

Page  300. 

2. 

$3753.60. 

3. 

$303300. 

4. 

$3177.72. 

5. 

$743.88. 

Pages  309-314. 


1. 


93. 

155TX3  of  eac 
8tV|  mo. 
4.27  mo. 

A,  $11317 ; 

B,  $9053.60 

C,  $6224.35 

D,  $6224.35 

E,  $6224.35 

F,  $622435. 
65  each. 
313  horses ; 
$61  each. 
247  yds. ; 
$1151.25  cost. 
108  A.  left ; 
$3  per  A. 
150  men. 
1152597  bbls. 
690  lbs.  left ; 
$0,571  per  lb. 
$5,618  per  head. 
32  spoons  of  each. 
49  animals. 


10. 
11. 
12. 

13. 
14. 
15. 

16.  48  feet, 

17.  $21428.57. 

18.  $480,305. 

19.  $240. 

20.  190  sq.  ft. 

21.  $94.41  Net  g. 

22.  U.  S.  3's  =  2ff  %  ; 

.  B.&0.6's=4Hf#§%. 

23.  .05TV 

24.  3534.3  lbs. 

25.  96  rods. 

26.  8s.  101-d.  per  yd. 

27.  $10566.43  gain. 

28.  8*f#. 

29.  71  mo. 

30.  $500  for  15  yrs. ; 
$1378.9162  greater. 

31.  7%  bonds; 
$10061  better. 

32.  8.807+  miles. 

33.  90*. 

34.  172.66  shares. 

35.  $4200,  1st  ; 
$3900,  2nd ; 
$3640,  3rd. 

36.  45+ fo. 

37.  $264.25. 

38.  $1838.8745. 

39.  $290  gain. 


40.  $8.25  on  2  mo; 
81  cts.  per  bbl. 

better. 

41.  79315.2  gals.; 
$3569.184  val. 

42.  12i%. 

43.  $891,493  loss. 

44.  $118^  per  share. 

45.  4,£T%. 

46.  $900,  A's  money  : 
$720,  B's      " 
$240,  C's      " 

47.  a  i«w ; 

f  £  greater. 

48.  f  of  the  mine. 

49.  20  days  A; 
30     "     B; 

50.  322  lots. 

51.  6^%. 

52.  396096  Pop. 

53.  43%  B; 
68%  C. 

54.  28+  %  N.  Y. 

55.  $3438.75. 

56.  75%. 

57.  66|%  Gold; 
33J%  Silver. 

58.  20'books. 

59.  26250  oz.  gold  ; 
2916|  oz.  alloy. 

60.  1900,  1st ; 
2660,  2nd  ; 
3420,  3rd. 

61.  $54000. 

62.  $65331 

63.  21050." 

64.  $10097|,  1st  cost ; 
$12347y,  2nd  cost 
.012+%  gain. 

65.  80|%. 

66.  $12.32  marked. 

67.  26iyds. 

68.  3691  §f$  times; 
14.6608  ft.  cir. 

69.  $18.20. 

70.  $387.88  +  . 

71.  $450,  C's  money  ; 
$800,  D's      " 

72.  53  days. 

73.  $473.45  due. 

74.  $11560.69. 

75.  9%. 

76.  $53,196. 

77.  16|%. 


Answers. 


331 


78. 


$1500,  daughter's 

$1050.85||,  C's 

82. 

486.6  bags. 

share  ; 

salvage  ; 

83. 

H%. 

$7500,  each  son's  ; 

$1784.1  lgV,  A's  loss; 

84. 

$413.50. 

$10000,  widow. 

$1529.24|f,  B's    " 

85. 

$2313.72. 

$1108.88|f,  A's 

$1709.15i|.  C's     " 

86. 

Wf%  gain 

salvage ; 

80. 

$708.75  di'f. 

87. 

Oct,  31. 

$945,761-8,  B's 

81. 

$189.03  Bal. 

88. 

$287.55. 

salvage  ; 

■# 


o 


o 


* 


A  Hand-Book  of  Mythology : 

Myths  and  Legends  op  Ancient  Greece  and  Rome.     Illustrated 
from  Antique  Sculptures.     By  E.  M.  Berens.   330  pp.    16mo,  cloth. 

The  author  in  this  volume  gives  in  a  very  graphic  way  a  lifelike  pic- 
ture of  the  deities  of  classical  times  as  they  were  conceived  and  worshiped 
by  the  ancients  themselves,  and  thereby  aims  to  awaken  in  the  minds  of 
young  students  a  desire  to  become  more  intimately  acquainted  with  the 
noble  productions  of  classical  antiquity. 

In  the  legends  which  form  the  second  portion  of  the  work,  a  picture,  as 
it  were,  is  given  of  old  Greek  life;  its  customs,  its  superstitions,  and  its 
princely  hospitalities  at  greater  length  than  is  usual  in  works  of  the  kind. 

In  a  chapter  devoted  to  the  purpose,  some  interesting  particulars  have 
been  collected  respecting  the  public  worship  of  the  ancient  Greeks  and 
Romans,  to  which  is  subjoined  an  account  of  their  principal  festivals.      , 

The  greatest  care  has  been  taken  that  no  single  passage  should  occur 
throughout  the  work  which  could  possibly  offend  the  most  scrupulous  deli- 
cacy, for  which  reason  it  may  safely  be  placed  in  the  hands  ot  the  young. 


RECOMMENDATIONS. 

"  Fifty  years  ago  compends  of  mythology  were  as  common  as  they  were  useful, 
but  of  late  the  youthful  student  has  been  relegated  to  the  classical  dictionary  for  the 
information  which  he  needs  at  every  step  of  his  progress.  The  legends  and 
myths  of  Greece  and  Rome  are  interwoven  with  our  literature,  and  the  general 
reader,  as  well  as  the  classical  student,  is  in  need  of  constant  assistance  to  enable 
him  to  appreciate  the  allusions  he  meets  with  on  almost  every  page.  The  classical 
dictionary  is  not  always  at  hand,  nor  is  there  always  time  to  find  what  is  wanted 
amid  its  full  derails,  and  the  reader  is  thus  often  obliged  to  answer  "no"  to  the 
question,  "  Understandest  thou  what  thou  readest  ?  "  This  handbook,  by  Mr. 
Berens,  is  intended  to  obviate  the  difficulty  and  to  supply  a  want.  It  is  compact, 
and  at  the  same  time  complete,  and  makes  a  neat  volume  for  the  study  table.  It 
gives  an  account  of  the  Greek  and  Roman  Divinities,  both  Majores  and  Minores, 
of  their  worship  and  the  festivals  devoted  to  them,  and  closes  with  sixteen  classical 
legends,  beginning  with  Cadmus,  who  sowed  the  dragon's  teeth  which  sprang  up 
into  armed  men,  and  ending  with  a  wifely  devotion  of  Penelope  and  its  reward. 
The  volume  is  not  one  of  mere  dry  detail,  but  is  enlivened  with  pictures  of  classi- 
cal life,  and  its  illustrations  from  ancient  sculpture  add  greatly  to  its  interest."— 
"  The  Churchman"  New  York  City.  ~ 

"  The  importance  of  a  knowledge  of  the  myths  and  legends  of  ancient  Greece 
and  Rome  is  fully  recognized  by  all  classical  teachers  and  students,  and  aiso  by  the 
intelligent  general  reader  ;  for  our  poems,  novels,  and  even  our  daily  newspapers 
abound  in  classical  allusions  which  this  work  of  Mr.  Berens'  fully  explains.  It 
is  appropriately  illustrated  from  antique  sculptures,  and  arranged  to  cover  the  first, 
second  and  third  dynasties,  the  Olympian  divinities,  Sea  Divinities,  Minor  and 
Roman  divinities.  It  also  explains  the  public  worship  of  the  ancient  Greeks  and 
Romans,  the  Greek  and  Roman  festivals.  Part  II.  is  devoted  to  the  legends  of  the 
ancients,  with  illustrations.  Every  page  of  this  book  is  interesting  and  instruc- 
tive, and  will  be  found  a  valuable  introduction  to  the  study  of  classic  authors  and 
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wisely  condensed  into  a  convenient-sized  book,  12mo,  330  pages,  beautifully 
printed  and  tastefully  bound."—"  Jovrnal  of  Education,"  Boston,  Mass. 

"  It  is  an  admirable  work  for  students  who  d(j§|re-Jto  find  in  printed  form  the 
facts  of  classic  mythology."— Rev.  L.  Clark  SeelyeTWUfrSmith  College,  Northamp- 
ton,  Mass. 

"  The  subject  is  a  difficult  one  from  the  nature  and  extent  of  the  materials  and 
the  requirements  of  our  schools.  The  author  avoids  extreme  theories  and  states 
clearly  the  facts  with  modest  limits  of  interpretation.  I  think  the  book  will  take 
well  and  wear  well."—  C.  F.  P.  Bancroft,  Ph.D.,  Prin.  Phillips  Academy,  Andover, 

Price,  by-Maii*  Post-paid,  $1.00. 

CLARK  &  MAYNARD,  Publishers,  New  York. 


ID     I /^Jo 


Two-Book  Series  of  Arithmetics. 

By  James  B.  Thomson,  LL.D.,  author  of  a  Mathematical  Course. 

1.  FIRST    LESSONS   IN   ARITHMETIC,   Oral    and    Written. 

Fully  and  handsomely  illustrated.    For  Primary  Schools.    144  pp. 
16mo,  cloth. 

2.  A  COMPLETE   GRADED  ARITHMETIC,  Oral  and  Writ- 

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following  embrace  some  of  the  characteristic  features  of  the  books : 


>m- 
on, 
ace 


i    la 

T35 


the 
ect 


for 
ad, 


div 
Sec 
fro 

bin 
anc 
wit 


Wr 
two 
acti 
roa 

him 

inst  la- 

tum ) 

con . in- 

cipl 

jps 

in  tfl  ?ar 

and 

xne  discussion  or  topics  wmcn  UBJUllg  exclusively  to  tne  nigner  uepart- 
ments  of  the  science  is  avoided ;  while  subjects  deemed  too  difficult  to  be 
appreciated  by  beginners,  but  important  for  them  when  more  advanced, 
are  placed  in  the  Appendix,  to  be  used  at  the  discretion  of  the  teacher. 

Arithmetical  puzzles  and  paradoxes,  and  problems  relating-  to  subjects 
having-  a  demoralizing  tendency,  as  gambling,  etc.,  are  excluded.  All  that 
is  obsolete  in  the  former  Tables  of  Weights  and  Measures  is  eliminated,  and 
the  part  retained  is  corrected  in  accordance  with  present  law  and  usage. 

Examples  for  Practice,  Problems  for  Review,  and  Test  Questions  are 
abundant  in  number  and  variety,  and  all  are  different  from  those  in  the 
author's  Practical  Arithmetic. 

The  arrangement  of  subjects  is  systematic ;  no  principle  is  anticipated, 
or  used  in  the.  explanation  of  another,  until  it  has  itself  been  explained. 
Subjects  intimately  connected  are  grouped  together  in  the  order  of  their 
dependence. 

Teachers  and  School  Officers,  who  are  dissatisfied  with  the  Arith- 
metics they  have  in  use,  are  invited  to  confer  with  the  publishers. 

CLARK  &  MAYNARD,  Publishers,  New  York. 


